A mathematician and a physicist were asked the following question:
<BR>
<BR>Suppose you walked by a burning house and saw a hydrant and
<BR>a hose not connected to the hydrant. What would you do?
<BR>
<BR>P: I would attach the hose to the hydrant, turn on the water, and put out
<BR>the fire.
<BR>
<BR>M: I would attach the hose to the hydrant, turn on the water, and put out
<BR>the fire.
<BR>
<BR>Then they were asked this question:
<BR>
<BR>Suppose you walked by a house and saw a hose connected to
<BR>a hydrant. What would you do?
<BR>
<BR>P: I would keep walking, as there is no problem to solve.
<BR>
<BR>M: I would disconnect the hose from the hydrant and set the house on fire,
<BR>reducing the problem to a previously solved form.
<BR>[addsig]

Eccone alcune:
<BR>
<BR><DIV style=\"font-size:0.5pt;font-family:Arial\">
<BR>----------
<BR>The USDA once wanted to make cows produce milk faster, to improve the
<BR>dairy industry.
<BR>
<BR>So, they decided to consult the foremost biologists and recombinant
<BR>DNA technicians to build them a better cow. They assembled this team
<BR>of great scientists, and gave them unlimited funding. They requested
<BR>rare chemicals, weird bacteria, tons of quarantine equipment, there
<BR>was a horrible typhus epidemic they started by accident, and, 2 years
<BR>later, they came back with the \"new, improved cow.\" It had a milk
<BR>production improvement of 2% over the original.
<BR>
<BR>They then tried with the greatest Nobel Prize winning chemists around.
<BR>They worked for six months, and, after requisitioning tons of chemical
<BR>equipment, and poisoning half the small town in Colorado where they
<BR>were working with a toxic cloud from one of their experiments, they
<BR>got a 5% improvement in milk output.
<BR>
<BR>The physicists tried for a year, and, after ten thousand cows were
<BR>subjected to radiation therapy, they got a 1% improvement in output.
<BR>
<BR>Finally, in desperation, they turned to the mathematicians. The
<BR>foremost mathematician of his time offered to help them with the
<BR>problem. Upon hearing the problem, he told the delegation that they
<BR>could come back in the morning and he would have solved the problem.
<BR>In the morning, they came back, and he handed them a piece of paper
<BR>with the computations for the new, 300% improved milk cow.
<BR>
<BR>The plans began:
<BR>
<BR>\"A Proof of the Attainability of Increased Milk Output from Bovines:
<BR>
<BR>Consider a spherical cow......\"
<BR>
<BR>----------
<BR>An engineer, a mathematician, and a physicist went to the races one
<BR>Saturday and laid their money down. Commiserating in the bar after
<BR>the race, the engineer says, \"I don\'t understand why I lost all my
<BR>money. I measured all the horses and calculated their strength and
<BR>mechanical advantage and figured out how fast they could run...\"
<BR>
<BR>The physicist interrupted him: \"...but you didn\'t take individual
<BR>variations into account. I did a statistical analysis of their
<BR>previous performances and bet on the horses with the highest
<BR>probability of winning...\"
<BR>
<BR>\"...so if you\'re so hot why are you broke?\" asked the engineer. But
<BR>before the argument can grow, the mathematician takes out his pipe and
<BR>they get a glimpse of his well-fattened wallet. Obviously here was a
<BR>man who knows something about horses. They both demanded to know his
<BR>secret.
<BR>
<BR>\"Well,\" he says, between puffs on the pipe, \"first I assumed all the
<BR>horses were identical and spherical...\"
<BR>
<BR>----------
<BR>Theorem : All positive integers are equal.
<BR>
<BR>Proof : Sufficient to show that for any two positive integers, A and B,
<BR>A = B. Further, it is sufficient to show that for all N > 0, if A
<BR>and B (positive integers) satisfy (MAX(A, B) = N) then A = B.
<BR>
<BR>Proceed by induction.
<BR>
<BR>If N = 1, then A and B, being positive integers, must both be 1.
<BR>So A = B.
<BR>
<BR>Assume that the theorem is true for some value k. Take A and B
<BR>with MAX(A, B) = k+1. Then MAX((A-1), (B-1)) = k. And hence
<BR>(A-1) = (B-1). Consequently, A = B.
<BR>
<BR>----------
<BR>A bunch of Polish scientists decided to flee their repressive
<BR>government by hijacking an airliner and forcing the pilot to fly them
<BR>to a western country. They drove to the airport, forced their way on
<BR>board a large passenger jet, and found there was no pilot on board.
<BR>Terrified, they listened as the sirens got louder. Finally, one of
<BR>the scientists suggested that since he was an experimentalist, he
<BR>would try to fly the aircraft.
<BR>
<BR>He sat down at the controls and tried to figure them out. The sirens
<BR>got louder and louder. Armed men surrounded the jet. The would be
<BR>pilot\'s friends cried out, \"Please, please take off now!!!
<BR>Hurry!!!!!!\"
<BR>
<BR>The experimentalist calmly replied, \"Have patience. I\'m just a simple
<BR>pole in a complex plane.\"
<BR>
<BR>----------
<BR>A group of Polish tourists is flying on a small airplane through the
<BR>Grand Canyon on a sightseeing tour. The tour guide announces: \"On the
<BR>right of the airplane, you can see the famous Bright Angle Falls.\"
<BR>The tourists leap out of their seats and crowd to the windows on the
<BR>right side. This causes a dynamic imbalance, and the plane violently
<BR>rolls to the side and crashes into the canyon wall. All aboard are
<BR>lost. The moral to this episode is: always keep your poles off the
<BR>right side of the plane.
<BR>
<BR>----------
<BR>Hiawatha Designs an Experiment
<BR>
<BR>Hiawatha, mighty hunter,
<BR>He could shoot ten arrows upward,
<BR>Shoot them with such strength and swiftness
<BR>That the last had left the bow-string
<BR>Ere the first to earth descended.
<BR>
<BR>This was commonly regarded
<BR>As a feat of skill and cunning.
<BR>Several sarcastic spirits
<BR>Pointed out to him, however,
<BR>That it might be much more useful
<BR>If he sometimes hit the target.
<BR>\"Why not shoot a little straighter
<BR>And employ a smaller sample?\"
<BR>Hiawatha, who at college
<BR>Majored in applied statistics,
<BR>Consequently felt entitled
<BR>To instruct his fellow man
<BR>In any subject whatsoever,
<BR>Waxed exceedingly indignant,
<BR>Talked about the law of errors,
<BR>Talked about truncated normals,
<BR>Talked of loss of information,
<BR>Talked about his lack of bias,
<BR>Pointed out that (in the long run)
<BR>Independent observations,
<BR>Even though they missed the target,
<BR>Had an average point of impact
<BR>Very near the spot he aimed at,
<BR>With the possible exception
<BR>of a set of measure zero.
<BR>
<BR>\"This,\" they said, \"was rather doubtful;
<BR>Anyway it didn\'t matter.
<BR>What resulted in the long run:
<BR>Either he must hit the target
<BR>Much more often than at present,
<BR>Or himself would have to pay for
<BR>All the arrows he had wasted.\"
<BR>
<BR>Hiawatha, in a temper,
<BR>Quoted parts of R. A. Fisher,
<BR>Quoted Yates and quoted Finney,
<BR>Quoted reams of Oscar Kempthorne,
<BR>Quoted Anderson and Bancroft
<BR>(practically in extenso)
<BR>Trying to impress upon them
<BR>That what actually mattered
<BR>Was to estimate the error.
<BR>
<BR>Several of them admitted:
<BR>\"Such a thing might have its uses;
<BR>Still,\" they said, \"he would do better
<BR>If he shot a little straighter.\"
<BR>
<BR>Hiawatha, to convince them,
<BR>Organized a shooting contest.
<BR>Laid out in the proper manner
<BR>Of designs experimental
<BR>Recommended in the textbooks,
<BR>Mainly used for tasting tea
<BR>(but sometimes used in other cases)
<BR>Used factorial arrangements
<BR>And the theory of Galois,
<BR>Got a nicely balanced layout
<BR>And successfully confounded
<BR>Second order interactions.
<BR>
<BR>All the other tribal marksmen,
<BR>Ignorant benighted creatures
<BR>Of experimental setups,
<BR>Used their time of preparation
<BR>Putting in a lot of practice
<BR>Merely shooting at the target.
<BR>
<BR>Thus it happened in the contest
<BR>That their scores were most impressive
<BR>With one solitary exception.
<BR>This, I hate to have to say it,
<BR>Was the score of Hiawatha,
<BR>Who as usual shot his arrows,
<BR>Shot them with great strength and swiftness,
<BR>Managing to be unbiased,
<BR>Not however with a salvo
<BR>Managing to hit the target.
<BR>
<BR>\"There!\" they said to Hiawatha,
<BR>\"That is what we all expected.\"
<BR>Hiawatha, nothing daunted,
<BR>Called for pen and called for paper.
<BR>But analysis of variance
<BR>Finally produced the figures
<BR>Showing beyond all peradventure,
<BR>Everybody else was biased.
<BR>And the variance components
<BR>Did not differ from each other\'s,
<BR>Or from Hiawatha\'s.
<BR>(This last point it might be mentioned,
<BR>Would have been much more convincing
<BR>If he hadn\'t been compelled to
<BR>Estimate his own components
<BR>>From experimental plots on
<BR>Which the values all were missing.)
<BR>
<BR>Still they couldn\'t understand it,
<BR>So they couldn\'t raise objections.
<BR>(Which is what so often happens
<BR>with analysis of variance.)
<BR>All the same his fellow tribesmen,
<BR>Ignorant benighted heathens,
<BR>Took away his bow and arrows,
<BR>Said that though my Hiawatha
<BR>Was a brilliant statistician,
<BR>He was useless as a bowman.
<BR>As for variance components
<BR>Several of the more outspoken
<BR>Make primeval observations
<BR>Hurtful of the finer feelings
<BR>Even of the statistician.
<BR>
<BR>In a corner of the forest
<BR>Sits alone my Hiawatha
<BR>Permanently cogitating
<BR>On the normal law of errors.
<BR>Wondering in idle moments
<BR>If perhaps increased precision
<BR>Might perhaps be sometimes better
<BR>Even at the cost of bias,
<BR>If one could thereby now and then
<BR>Register upon a target.
<BR>
<BR>W. E. Mientka, \"Professor Leo Moser -- Reflections of a Visit\"
<BR>American Mathematical Monthly, Vol. 79, Number 6 (June-July, 1972)
<BR>
<BR>See also \"Applied Dynamic Programming\" by Bellman and Dreyfuss, prior to 1962.
<BR>
<BR>----------
<BR>An assemblage of the most gifted minds in the world were all posed the
<BR>following question:
<BR>
<BR>\"What is 2 * 2 ?\"
<BR>
<BR>The engineer whips out his slide rule (so it\'s old) and shuffles it
<BR>back and forth, and finally announces \"3.99\".
<BR>
<BR>The physicist consults his technical references, sets up the problem
<BR>on his computer, and announces \"it lies between 3.98 and 4.02\".
<BR>
<BR>The mathematician cogitates for a while, oblivious to the rest of the
<BR>world, then announces: \"I don\'t what the answer is, but I can tell
<BR>you, an answer exists!\".
<BR>
<BR>Philosopher: \"But what do you _mean_ by 2 * 2 ?\"
<BR>
<BR>Logician: \"Please define 2 * 2 more precisely.\"
<BR>
<BR>Accountant: Closes all the doors and windows, looks around carefully,
<BR>then asks \"What do you _want_ the answer to be?\"
<BR>
<BR>Computer Hacker: Breaks into the NSA super-computer and gives the answer.
<BR>
<BR>----------
<BR>Economist: Someone who is good with numbers but lacks the personality
<BR>to be an accountant.
<BR>
<BR>----------
<BR>Old mathematicians never die; they just lose some of their functions.
<BR>
<BR>----------
<BR>During a class of calculus my lecturer suddenly checked himself and
<BR>stared intently at the table in front of him for a while. Then he
<BR>looked up at us and explained that he thought he had brought six piles
<BR>of papers with him, but \"no matter how he counted\" there was only five
<BR>on the table. Then he became silent for a while again and then told
<BR>the following story:
<BR>
<BR>\"When I was young in Poland I met the great mathematician Waclaw
<BR>Sierpinski. He was old already then and rather absent-minded. Once he
<BR>had to move to a new place for some reason. His wife wife didn\'t trust
<BR>him very much, so when they stood down on the street with all their
<BR>things, she said:
<BR>- Now, you stand here and watch our ten trunks, while I go and get a
<BR>taxi.
<BR>
<BR>She left and left him there, eyes somewhat glazed and humming
<BR>absently. Some minutes later she returned, presumably having called
<BR>for a taxi. Says Mr. Sierpinski (possibly with a glint in his eye):
<BR>- I thought you said there were ten trunks, but I\'ve only counted to nine.
<BR>- No, they\'re TEN!
<BR>- No, count them: 0, 1, 2, ...\"
<BR>
<BR>-----------
<BR>What\'s non-orientable and lives in the sea?
<BR>
<BR>Mobius Dick.
<BR>
<BR>----------
<BR>Philosopher: \"Resolution of the continuum hypothesis will have
<BR>profound implications to all of science.\"
<BR>
<BR>Physicist: \"Not quite. Physics is well on its way without those
<BR>mythical `foundations\'. Just give us serviceable mathematics.\"
<BR>
<BR>Computer Scientist:
<BR>\"Who cares? Everything in this Universe seems to be finite
<BR>anyway. Besides, I\'m too busy debugging my Pascal programs.\"
<BR>
<BR>Mathematician:
<BR>\"Forget all that! Just make your formulae as aesthetically
<BR>pleasing as possible!\"
<BR>
<BR>-----------
<BR>Definition:
<BR>
<BR>Jogging girl scout = Brownian motion.
<BR>
<BR>----------
<BR>lim sin(x)
<BR>n --> oo ------ = 6
<BR>n
<BR>
<BR>Proof: cancel the n in the numerator and denominator.
<BR>
<BR>-----------
<BR>Two male mathematicians are in a bar.
<BR>
<BR>The first one says to the second that the average person knows very
<BR>little about basic mathematics.
<BR>
<BR>The second one disagrees, and claims that most people can cope with a
<BR>reasonable amount of math.
<BR>
<BR>The first mathematician goes off to the washroom, and in his absence
<BR>the second calls over the waitress.
<BR>
<BR>He tells her that in a few minutes, after his friend has returned, he
<BR>will call her over and ask her a question. All she has to do is
<BR>answer one third x cubed.
<BR>
<BR>She repeats `one thir -- dex cue\'? He repeats `one third x cubed\'.
<BR>
<BR>Her: `one thir dex cuebd\'? Yes, that\'s right, he says. So she
<BR>agrees, and goes off mumbling to herself, `one thir dex cuebd...\'.
<BR>
<BR>The first guy returns and the second proposes a bet to prove his
<BR>point, that most people do know something about basic math.
<BR>
<BR>He says he will ask the blonde waitress an integral, and the first
<BR>laughingly agrees.
<BR>
<BR>The second man calls over the waitress and asks `what is the integral
<BR>of x squared?\'.
<BR>
<BR>The waitress says `one third x cubed\' and while walking away, turns
<BR>back and says over her shoulder `plus a constant\'!
<BR>
<BR>----------
<BR>This was made by Mike Bender and Sarah Herr:
<BR>
<BR>MATHEMATICS PURITY TEST
<BR>
<BR>Count the number of yes\'s, subtract from 60, and divide by 0.6.
<BR>
<BR>----------
<BR>
<BR>The Basics
<BR>
<BR>1) Have you ever been excited about math?
<BR>2) Had an exciting dream about math?
<BR>3) Made a mathematical calculation?
<BR>4) Manipulated the numerator of an equation?
<BR>5) Manipulated the denominator of an equation?
<BR>6) On your first problem set?
<BR>7) Worked on a problem set past 3:00 a.m.?
<BR><IMG SRC="images/forum/icons/icon_cool.gif"> Worked on a problem set all night?
<BR>9) Had a hard problem?
<BR>10) Worked on a problem continuously for more than 30 minutes?
<BR>11) Worked on a problem continuously for more than four hours?
<BR>12) Done more than one problem set on the same night (i.e. both
<BR>started and finished them)?
<BR>13) Done more than three problem sets on the same night?
<BR>14) Taken a math course for a full year?
<BR>15) Taken two different math courses at the same time?
<BR>16) Done at least one problem set a week for more than four months?
<BR>17) Done at least one problem set a night for more than one month
<BR>(weekends excluded)?
<BR>1<IMG SRC="images/forum/icons/icon_cool.gif"> Done a problem set alone?
<BR>19) Done a problem set in a group of three or more?
<BR>20) Done a problem set in a group of 15 or more?
<BR>21) Was it mixed company?
<BR>22) Have you ever inadvertently walked in upon people doing a problem set?
<BR>23) And joined in afterwards?
<BR>24) Have you ever used food doing a problem set?
<BR>25) Did you eat it all?
<BR>26) Have you ever had a domesticated pet or animal walk over you while you
<BR>were doing a problem set?
<BR>27) Done a problem set in a public place where you might be discovered?
<BR>2<IMG SRC="images/forum/icons/icon_cool.gif"> Been discovered while doing a problem set?
<BR>
<BR>
<BR>Kinky Stuff
<BR>
<BR>29) Have you ever applied your math to a hard science?
<BR>30) Applied your math to a soft science?
<BR>31) Done an integration by parts?
<BR>32) Done two integration by parts in a single problem?
<BR>33) Bounded the domain and range of your function?
<BR>34) Used the domination test for improper integrals?
<BR>35) Done Newton\'s Method?
<BR>36) Done the Method of Frobenius?
<BR>37) Used the Sandwich Theorem?
<BR>3<IMG SRC="images/forum/icons/icon_cool.gif"> Used the Mean Value Theorem?
<BR>39) Used a Gaussian surface?
<BR>40) Used a foreign object on a math problem (eg: calculator)?
<BR>41) Used a program to improve your mathematical technique (eg: MACSYMA)?
<BR>42) Not used brackets when you should have?
<BR>43) Integrated a function over its full period?
<BR>44) Done a calculation in three-dimensional space?
<BR>45) Done a calculation in n-dimensional space?
<BR>46) Done a change of bases?
<BR>47) Done a change of bases specifically in order to magnify your vector?
<BR>4<IMG SRC="images/forum/icons/icon_cool.gif"> Worked through four complete bases in a single night (eg: using the
<BR>Graham-Schmidt method)?
<BR>49) Inserted a number into an equation?
<BR>50) Calculated the residue of a pole?
<BR>51) Scored perfectly on a math test?
<BR>52) Swallowed everything your professor gave you?
<BR>53) Used explicit notation in your problem set?
<BR>54) Purposefully omitted important steps in your problem set?
<BR>55) Padded your own problem set?
<BR>56) Been blown away on a test?
<BR>57) Blown away your professor on a test?
<BR>5<IMG SRC="images/forum/icons/icon_cool.gif"> Have you ever multiplied 23 by 3?
<BR>59) Have you ever bounded your Bessel function so that the membrane
<BR>did not shoot to infinity?
<BR>69) Have you ever understood the following quote:
<BR>\"The relationship between Z^0 to C_0, B_0, and H_0
<BR>is an example of a general principle which we have
<BR>encountered: the kernel of the adjoint of a linear
<BR>transformation is both the annihilator space of the
<BR>image of the transformation and also the dual space
<BR>of the quotient of the space of which the image is
<BR>a subspace by the image subspace.\"
<BR>(Sternberg & Bamberg\'s _A \"Course\" in Mathematics for
<BR>Students of Physics_, vol. 2)
<BR>
<BR>
<BR>-----------
<BR>
<BR>A somewhat advanced society has figured how to package basic knowledge
<BR>in pill form.
<BR>
<BR>A student, needing some learning, goes to the pharmacy and asks what
<BR>kind of knowledge pills are available. The pharmacist says \"Here\'s a
<BR>pill for English literature.\" The student takes the pill and swallows
<BR>it and has new knowledge about English literature!
<BR>
<BR>\"What else do you have?\" asks the student.
<BR>
<BR>\"Well, I have pills for art history, biology, and world history,\"
<BR>replies the pharmacist.
<BR>
<BR>The student asks for these, and swallows them and has new knowledge
<BR>about those subjects.
<BR>
<BR>Then the student asks, \"Do you have a pill for math?\"
<BR>
<BR>The pharmacist says \"Wait just a moment\", and goes back into the
<BR>storeroom and brings back a whopper of a pill and plunks it on the
<BR>counter.
<BR>
<BR>\"I have to take that huge pill for math?\" inquires the student.
<BR>
<BR>The pharmacist replied \"Well, you know math always was a little hard
<BR>to swallow.\"
<BR>
<BR>-----------
<BR>\"A mathematician is a device for turning coffee into theorems\"
<BR>-- P. Erdos
<BR>
<BR>-----------
<BR>
<BR>Three standard Peter Lax jokes (heard in his lectures) :
<BR>
<BR>1. What\'s the contour integral around Western Europe?
<BR>Answer: Zero, because all the Poles are in Eastern Europe!
<BR>Addendum: Actually, there ARE some Poles in Western Europe, but
<BR>they are removable!
<BR>
<BR>2. An English mathematician (I forgot who) was asked by his very religious
<BR>colleague:
<BR>Do you believe in one God?
<BR>Answer: Yes, up to isomorphism!
<BR>
<BR>3. What is a compact city?
<BR>It\'s a city that can be guarded by finitely many near-sighted
<BR>policemen!
<BR>
<BR>-----------
<BR>\"Algebraic symbols are used when you do not know what you are talking about.\"
<BR>
<BR>-----------
<BR>Heisenberg might have slept here.
<BR>
<BR>Moebius always does it on the same side.
<BR>
<BR>Statisticians probably do it
<BR>
<BR>Algebraists do it in groups.
<BR>
<BR>(Logicians do it) or [not (logicians do it)].
<BR>
<BR>-----------
<BR>A promising PhD candidate was presenting his thesis at his final
<BR>examination. He proceeded with a derivation and ended up with
<BR>something like:
<BR>
<BR>F = -MA
<BR>
<BR>He was embarrassed, his supervising professor was embarrassed, and the
<BR>rest of the committee was embarrassed. The student coughed nervously
<BR>and said \"I seem to have made a slight error back there somewhere.\"
<BR>
<BR>One of the mathematicians on the committee replied dryly, \"Either that
<BR>or an odd number of them!\"
<BR>
<BR>-----------
<BR>There was a mad scientist ( a mad ...social... scientist ) who
<BR>kidnapped three colleagues, an engineer, a physicist, and a
<BR>mathematician, and locked each of them in seperate cells with plenty
<BR>of canned food and water but no can opener.
<BR>
<BR>A month later, returning, the mad scientist went to the engineer\'s
<BR>cell and found it long empty. The engineer had constructed a can
<BR>opener from pocket trash, used aluminum shavings and dried sugar to
<BR>make an explosive, and escaped.
<BR>
<BR>The physicist had worked out the angle necessary to knock the lids off
<BR>the tin cans by throwing them against the wall. She was developing a
<BR>good pitching arm and a new quantum theory.
<BR>
<BR>The mathematician had stacked the unopened cans into a surprising
<BR>solution to the kissing problem; his desiccated corpse was propped
<BR>calmly against a wall, and this was inscribed on the floor in blood:
<BR>
<BR>Theorem: If I can\'t open these cans, I\'ll die.
<BR>
<BR>Proof: assume the opposite...
<BR>
<BR>-----------
<BR>Problem: To Catch a Lion in the Sahara Desert.
<BR>
<BR>(Hunting lions in Africa was originally published as \"A contribution
<BR>to the mathematical theory of big game hunting\" in the American
<BR>Mathematical Monthly in 1938 by \"H. Petard, of Princeton NJ\" [actually
<BR>the late Ralph Boas]. It has been reprinted several times.
<BR>
<BR>1. Mathematical Methods
<BR>
<BR>1.1 The Hilbert (axiomatic) method
<BR>
<BR>We place a locked cage onto a given point in the desert. After that
<BR>we introduce the following logical system:
<BR>Axiom 1: The set of lions in the Sahara is not empty.
<BR>Axiom 2: If there exists a lion in the Sahara, then there exists a
<BR>lion in the cage.
<BR>Procedure: If P is a theorem, and if the following is holds:
<BR>\"P implies Q\", then Q is a theorem.
<BR>Theorem 1: There exists a lion in the cage.
<BR>
<BR>1.2 The geometrical inversion method
<BR>
<BR>We place a spherical cage in the desert, enter it and lock it from
<BR>inside. We then perform an inversion with respect to the cage. Then
<BR>the lion is inside the cage, and we are outside.
<BR>
<BR>1.3 The projective geometry method
<BR>
<BR>Without loss of generality, we can view the desert as a plane surface.
<BR>We project the surface onto a line and afterwards the line onto an
<BR>interior point of the cage. Thereby the lion is mapped onto that same
<BR>point.
<BR>
<BR>1.4 The Bolzano-Weierstrass method
<BR>
<BR>Divide the desert by a line running from north to south. The lion is
<BR>then either in the eastern or in the western part. Let\'s assume it is
<BR>in the eastern part. Divide this part by a line running from east to
<BR>west. The lion is either in the northern or in the southern part.
<BR>Let\'s assume it is in the northern part. We can continue this process
<BR>arbitrarily and thereby constructing with each step an increasingly
<BR>narrow fence around the selected area. The diameter of the chosen
<BR>partitions converges to zero so that the lion is caged into a fence of
<BR>arbitrarily small diameter.
<BR>
<BR>1.5 The set theoretical method
<BR>
<BR>We observe that the desert is a separable space. It therefore
<BR>contains an enumerable dense set of points which constitutes a
<BR>sequence with the lion as its limit. We silently approach the lion in
<BR>this sequence, carrying the proper equipment with us.
<BR>
<BR>1.6 The Peano method
<BR>
<BR>In the usual way construct a curve containing every point in the
<BR>desert. It has been proven [1] that such a curve can be traversed in
<BR>arbitrarily short time. Now we traverse the curve, carrying a spear,
<BR>in a time less than what it takes the lion to move a distance equal to
<BR>its own length.
<BR>
<BR>1.7 A topological method
<BR>
<BR>We observe that the lion possesses the topological gender of a torus.
<BR>We embed the desert in a four dimensional space. Then it is possible
<BR>to apply a deformation [2] of such a kind that the lion when returning
<BR>to the three dimensional space is all tied up in itself. It is then
<BR>completely helpless.
<BR>
<BR>1.8 The Cauchy method
<BR>
<BR>We examine a lion-valued function f(z). Be \\zeta the cage. Consider
<BR>the integral
<BR>
<BR>1 [ f(z)
<BR>------- I --------- dz
<BR>2 \\pi i ] z - \\zeta
<BR>
<BR>C
<BR>
<BR>where C represents the boundary of the desert. Its value is f(zeta),
<BR>i.e. there is a lion in the cage [3].
<BR>1.9 The Wiener-Tauber method
<BR>
<BR>We obtain a tame lion, L_0, from the class L(-\\infinity,\\infinity),
<BR>whose fourier transform vanishes nowhere. We put this lion somewhere
<BR>in the desert. L_0 then converges toward our cage. According to the
<BR>general Wiener-Tauner theorem [4] every other lion L will converge
<BR>toward the same cage. (Alternatively we can approximate L arbitrarily
<BR>close by translating L_0 through the desert [5].)
<BR>
<BR>2 Theoretical Physics Methods
<BR>
<BR>2.1 The Dirac method
<BR>
<BR>We assert that wild lions can ipso facto not be observed in the Sahara
<BR>desert. Therefore, if there are any lions at all in the desert, they
<BR>are tame. We leave catching a tame lion as an exercise to the reader.
<BR>
<BR>2.2 The Schroedinger method
<BR>
<BR>At every instant there is a non-zero probability of the lion being in
<BR>the cage. Sit and wait.
<BR>
<BR>2.3 The Quantum Measurement Method
<BR>
<BR>We assume that the sex of the lion is _ab initio_ indeterminate. The
<BR>wave function for the lion is hence a superposition of the gender
<BR>eigenstate for a lion and that for a lioness. We lay these eigenstates
<BR>out flat on the ground and orthogonal to each other. Since the (male)
<BR>lion has a distinctive mane, the measurement of sex can safely be made
<BR>from a distance, using binoculars. The lion then collapses into one of
<BR>the eigenstates, which is rolled up and placed inside the cage.
<BR>
<BR>2.4 The nuclear physics method
<BR>
<BR>Insert a tame lion into the cage and apply a Majorana exchange
<BR>operator [6] on it and a wild lion.
<BR>
<BR>As a variant let us assume that we would like to catch (for argument\'s
<BR>sake) a male lion. We insert a tame female lion into the cage and
<BR>apply the Heisenberg exchange operator [7], exchanging spins.
<BR>
<BR>2.5 A relativistic method
<BR>
<BR>All over the desert we distribute lion bait containing large amounts
<BR>of the companion star of Sirius. After enough of the bait has been
<BR>eaten we send a beam of light through the desert. This will curl
<BR>around the lion so it gets all confused and can be approached without
<BR>danger.
<BR>
<BR>3 Experimental Physics Methods
<BR>
<BR>3.1 The thermodynamics method
<BR>
<BR>We construct a semi-permeable membrane which lets everything but lions
<BR>pass through. This we drag across the desert.
<BR>
<BR>3.2 The atomic fission method
<BR>
<BR>We irradiate the desert with slow neutrons. The lion becomes
<BR>radioactive and starts to disintegrate. Once the disintegration
<BR>process is progressed far enough the lion will be unable to resist.
<BR>
<BR>3.3 The magneto-optical method
<BR>
<BR>We plant a large, lense shaped field with cat mint (nepeta cataria)
<BR>such that its axis is parallel to the direction of the horizontal
<BR>component of the earth\'s magnetic field. We put the cage in one of the
<BR>field\'s foci . Throughout the desert we distribute large amounts of
<BR>magnetized spinach (spinacia oleracea) which has, as everybody knows,
<BR>a high iron content. The spinach is eaten by vegetarian desert
<BR>inhabitants which in turn are eaten by the lions. Afterwards the
<BR>lions are oriented parallel to the earth\'s magnetic field and the
<BR>resulting lion beam is focussed on the cage by the cat mint lense.
<BR>
<BR>[1] After Hilbert, cf. E. W. Hobson, \"The Theory of Functions of a Real
<BR>Variable and the Theory of Fourier\'s Series\" (1927), vol. 1, pp 456-457
<BR>[2] H. Seifert and W. Threlfall, \"Lehrbuch der Topologie\" (1934), pp 2-3
<BR>[3] According to the Picard theorem (W. F. Osgood, Lehrbuch der
<BR>Funktionentheorie, vol 1 (192<IMG SRC="images/forum/icons/icon_cool.gif">, p 17<IMG SRC="images/forum/icons/icon_cool.gif"> it is possible to catch every lion
<BR>except for at most one.
<BR>[4] N. Wiener, \"The Fourier Integral and Certain of its Applications\" (1933),
<BR>pp 73-74
<BR>[5] N. Wiener, ibid, p 89
<BR>[6] cf e.g. H. A. Bethe and R. F. Bacher, \"Reviews of Modern Physics\", 8
<BR>(1936), pp 82-229, esp. pp 106-107
<BR>[7] ibid
<BR>
<BR>----------
<BR>
<BR>4 Contributions from Computer Science.
<BR>
<BR>4.1 The search method
<BR>
<BR>We assume that the lion is most likely to be found in the direction to
<BR>the north of the point where we are standing. Therefore the REAL
<BR>problem we have is that of speed, since we are only using a PC to
<BR>solve the problem.
<BR>
<BR>4.2 The parallel search method.
<BR>
<BR>By using parallelism we will be able to search in the direction to the
<BR>north much faster than earlier.
<BR>
<BR>4.3 The Monte-Carlo method.
<BR>
<BR>We pick a random number indexing the space we search. By excluding
<BR>neighboring points in the search, we can drastically reduce the number
<BR>of points we need to consider. The lion will according to probability
<BR>appear sooner or later.
<BR>
<BR>4.4 The practical approach.
<BR>
<BR>We see a rabbit very close to us. Since it is already dead, it is
<BR>particularly easy to catch. We therefore catch it and call it a lion.
<BR>
<BR>4.5 The common language approach.
<BR>
<BR>If only everyone used ADA/Common Lisp/Prolog, this problem would be
<BR>trivial to solve.
<BR>
<BR>4.6 The standard approach.
<BR>
<BR>We know what a Lion is from ISO 4711/X.123. Since CCITT have specified
<BR>a Lion to be a particular option of a cat we will have to wait for a
<BR>harmonized standard to appear. $20,000,000 have been funded for
<BR>initial investigations into this standard development.
<BR>
<BR>4.7 Linear search.
<BR>
<BR>Stand in the top left hand corner of the Sahara Desert. Take one step
<BR>east. Repeat until you have found the lion, or you reach the right
<BR>hand edge. If you reach the right hand edge, take one step
<BR>southwards, and proceed towards the left hand edge. When you finally
<BR>reach the lion, put it the cage. If the lion should happen to eat you
<BR>before you manage to get it in the cage, press the reset button, and
<BR>try again.
<BR>
<BR>4.8 The Dijkstra approach:
<BR>
<BR>The way the problem reached me was: catch a wild lion in the Sahara
<BR>Desert. Another way of stating the problem is:
<BR>
<BR>Axiom 1: Sahara elem deserts
<BR>Axiom 2: Lion elem Sahara
<BR>Axiom 3: NOT(Lion elem cage)
<BR>
<BR>We observe the following invariant:
<BR>
<BR>P1: C(L) v not(C(L))
<BR>
<BR>where C(L) means: the value of \"L\" is in the cage.
<BR>
<BR>Establishing C initially is trivially accomplished with the statement
<BR>
<BR>;cage := {}
<BR>
<BR>Note 0:
<BR>This is easily implemented by opening the door to the cage and shaking
<BR>out any lions that happen to be there initially.
<BR>(End of note 0.)
<BR>
<BR>The obvious program structure is then:
<BR>
<BR>;cage:={}
<BR>;do NOT (C(L)) ->
<BR>;\"approach lion under invariance of P1\"
<BR>;if P(L) ->
<BR>;\"insert lion in cage\"
<BR>[] not P(L) ->
<BR>;skip
<BR>;fi
<BR>;od
<BR>
<BR>where P(L) means: the value of L is within arm\'s reach.
<BR>
<BR>Note 1:
<BR>Axiom 2 ensures that the loop terminates.
<BR>(End of note 1.)
<BR>
<BR>Exercise 0:
<BR>Refine the step \"Approach lion under invariance of P1\".
<BR>(End of exercise 0.)
<BR>
<BR>Note 2:
<BR>The program is robust in the sense that it will lead to
<BR>abortion if the value of L is \"lioness\".
<BR>(End of note 2.)
<BR>
<BR>Remark 0: This may be a new sense of the word \"robust\" for you.
<BR>(End of remark 0.)
<BR>
<BR>Note 3:
<BR>
<BR>>From observation we can see that the above program leads to the
<BR>desired goal. It goes without saying that we therefore do not have to
<BR>run it.
<BR>(End of note 3.)
<BR>(End of approach.)
<BR>
<BR>----------
<BR>
<BR>For other articles, see also:
<BR>
<BR>A Random Walk in Science - R.L. Weber and E. Mendoza
<BR>More Random Walks In Science - R.L. Weber and E. Mendoza
<BR>In Mathematical Circles (2 volumes) - Howard Eves
<BR>Mathematical Circles Revisited - Howard Eves
<BR>Mathematical Circles Squared - Howard Eves
<BR>Fantasia Mathematica - Clifton Fadiman
<BR>The Mathematical Magpi - Clifton Fadiman
<BR>Seven Years of Manifold - Jaworski
<BR>The Best of the Journal of Irreproducible Results - George H. Scheer
<BR>Mathematics Made Difficult - Linderholm
<BR>A Stress-Analysis of a Strapless Evening Gown - Robert Baker
<BR>The Worm-Runners Digest
<BR>Knuth\'s April 1984 CACM article on The Space Complexity of Songs
<BR>Stolfi and ?? SIGACT article on Pessimal Algorithms and Simplexity Analysis
<BR>
<BR>-----------
<BR>Not a joke, but a humorous ditty I heard from some guys in an
<BR>engineering fraternity (to the best of my recollection):
<BR>
<BR>I\'ll do it phonetically:
<BR>
<BR>ee to the ex dee ex,
<BR>ee to the why dee why,
<BR>sine x, cosine x,
<BR>natural log of y,
<BR>derivative on the left
<BR>derivative on the right
<BR>integrate, integrate,
<BR>fight! fight! fight!
<BR>
<BR>----------
<BR>The Programmers\' Cheer --
<BR>
<BR>Shift to the left, shift to the right!
<BR>Pop up, push down, byte, byte, byte!
<BR>
<BR>----------
<BR>Other cheers:
<BR>
<BR>E to the x dx dy
<BR>radical transcendental pi
<BR>secant cosine tangent sine
<BR>3.14159
<BR>2.71828
<BR>come on folks let\'s integerate!!
<BR>
<BR>----------
<BR>
<BR>E to the i dx dy
<BR>E to y dy
<BR>cosine secant log of pi
<BR>disintegrate em RPI !!!
<BR>
<BR>----------
<BR>
<BR>square root, tangent
<BR>hyperbolic sine,
<BR>3.14159
<BR>e to the x, dy, dx,
<BR>sliderule, slipstick, TECH TECH TECH!
<BR>
<BR>----------
<BR>
<BR>e to the u, du/dx
<BR>e to the x dx
<BR>cosine, secant, tangent, sine,
<BR>3.14159
<BR>integral, radical, u dv,
<BR>slipstick, slide rule, MIT!
<BR>
<BR>----------
<BR>
<BR>E to the X
<BR>D-Y, D-X
<BR>E to the X
<BR>D-X.
<BR>Cosine, Secant, Tangent, Sine
<BR>3.14159
<BR>E-I, Radical, Pi
<BR>Fight\'em, Fight\'em, WPI!
<BR>
<BR>Go Worcester Polytechnic Institute!!!!!!
<BR>
<BR>----------
<BR>Words in {} should be interpreted as greek letters:
<BR>
<BR>Q: I M A {pi}{rho}Maniac. R U 1,2?
<BR>o <- read as \"U-not\"
<BR>A: Y ?
<BR>o
<BR>
<BR>(\"I am a pyromaniac. Are you not one, too?\" \"Why not?\")
<BR>
<BR>F U \\{can\\} \\{read\\} Ths U \\{Mst\\} \\{use\\} TeX
<BR>(\"If you can read this, you must use TeX\")
<BR>
<BR>----------
<BR>Three men are in a hot-air balloon. Soon, they find themselves lost
<BR>in a canyon somewhere. One of the three men says, \"I\'ve got an idea.
<BR>We can call for help in this canyon and the echo will carry our voices
<BR>far.\"
<BR>
<BR>So he leans over the basket and yells out, \"Helllloooooo! Where are
<BR>we?\" (They hear the echo several times.)
<BR>
<BR>15 minutes later, they hear this echoing voice: \"Helllloooooo! You\'re
<BR>lost!!\"
<BR>
<BR>One of the men says, \"That must have been a mathematician.\"
<BR>
<BR>Puzzled, one of the other men asks, \"Why do you say that?\"
<BR>
<BR>The reply: \"For three reasons. (1) he took a long time to answer, (2)
<BR>he was absolutely correct, and (3) his answer was absolutely useless.\"
<BR>
<BR>-----------
<BR>Actually, I prefer the IBM version of this joke...
<BR>
<BR>A small, 14-seat plane is circling for a landing in Atlanta. It\'s
<BR>totally fogged in, zero visibility, and suddenly there\'s a small
<BR>electrical fire in the cockpit which disables all of the instruments
<BR>and the radio. The pilot continues circling, totally lost, when
<BR>suddenly he finds himself flying next to a tall office building.
<BR>
<BR>He rolls down the window (this particular airplane happens to have
<BR>roll-down windows) and yells to a person inside the building, \"Where
<BR>are we?\"
<BR>
<BR>The person responds \"In an airplane!\"
<BR>
<BR>The pilot then banks sharply to the right, circles twice, and makes a
<BR>perfect landing at Atlanta International.
<BR>
<BR>As the passengers emerge, shaken but unhurt, one of them says to the
<BR>pilot, \"I\'m certainly glad you were able to land safely, but I don\'t
<BR>understand how the response you got was any use.\"
<BR>
<BR>\"Simple,\" responded the pilot. \"I got an answer that was completely
<BR>accurate and totally irrelevant to my problem, so I knew it had to be
<BR>the IBM building.\"
<BR>
<BR>-----------
<BR>(I\'m not sure if the following one is a true story or not)
<BR>The great logician Bertrand Russell (or was it A.N. Whitehead?)
<BR>once claimed that he could prove anything if given that 1+1=1.
<BR>So one day, some smarty-pants asked him, \"Ok. Prove that
<BR>you\'re the Pope.\"
<BR>He thought for a while and proclaimed, \"I am one. The Pope
<BR>is one. Therefore, the Pope and I are one.\"
<BR>
<BR>[NOTE: The following is from <a href=\"mailto:merritt@Gendev.slc.paramax.com\" target=\"_new\">merritt@Gendev.slc.paramax.com</a> (Merritt).
<BR>The story about 1+1=1 causing ridiculous consequences was, I believe,
<BR>originally the product of a conversation at the Trinity High Table.
<BR>It is recorded in Sir Harold Jeffreys\' Scientific Inference, in a note
<BR>to chapter one. Jeffreys remarks that the fact that everything
<BR>followed from a single contradiction had been noticed by Aristotle (I
<BR>doubt this way of putting it is quite correct, but that is beside the
<BR>point). He goes on to say that McTaggart denied the consequence: \"if
<BR>2+2=5, how can you prove that I am the pope?\" Hardy is supposed to
<BR>have replied: \"if 2+2=5, 4=5; subtract 3; then 1=2; but McTaggart and
<BR>the pope are two; therefore McTaggart and the pope are one.\" When I
<BR>consider this story, I am astonished at how much more brilliant some
<BR>people are than I (quite independent of the fallacies in the
<BR>argument).
<BR>
<BR>Since McTaggart, Hardy, Whitehead, and Russell (the last two of whom
<BR>were credited with a variant of Hardy\'s argument in your post) were
<BR>all fellows of Trinity and Jeffreys (their exact contemporary) was a
<BR>fellow of St. Johns, I suspect that (whatever the truth of Jeffreys\'
<BR>story) it is very unlikely that Whitehead or Russell had anything to do
<BR>with it. The extraordinary point to me about the story is that Hardy
<BR>was able to snap this argument out between mouthfuls, so to speak, and
<BR>he was not even a logician at all. This is probably why it came in
<BR>some people\'s minds to be attributed to one or other of the famous
<BR>Trinity logicians.
<BR>
<BR>---------
<BR>THE STORY OF BABEL:
<BR>
<BR>In the beginning there was only one kind of Mathematician, created by
<BR>the Great Mathematical Spirit form the Book: the Topologist. And they
<BR>grew to large numbers and prospered.
<BR>
<BR>One day they looked up in the heavens and desired to reach up as far
<BR>as the eye could see. So they set out in building a Mathematical
<BR>edifice that was to reach up as far as \"up\" went. Further and further
<BR>up they went ... until one night the edifice collapsed under the
<BR>weight of paradox.
<BR>
<BR>The following morning saw only rubble where there once was a huge
<BR>structure reaching to the heavens. One by one, the Mathematicians
<BR>climbed out from under the rubble. It was a miracle that nobody was
<BR>killed; but when they began to speak to one another, SUPRISE of all
<BR>surprises! they could not understand each other. They all spoke
<BR>different languages. They all fought amongst themselves and each went
<BR>about their own way. To this day the Topologists remain the original
<BR>Mathematicians.
<BR>
<BR>- adapted from an American Indian legend
<BR>of the Mound Of Babel
<BR>
<BR>----------
<BR>Methods of Mathematical Proof
<BR>
<BR>This is from _A Random Walk in Science_ (by Joel E. Cohen?):
<BR>
<BR>
<BR>To illustrate the various methods of proof we give an example of a
<BR>logical system.
<BR>
<BR>THE PEJORATIVE CALCULUS
<BR>
<BR>Lemma 1. All horses are the same colour.
<BR>(Proof by induction)
<BR>
<BR>Proof. It is obvious that one horse is the same colour. Let us assume
<BR>the proposition P(k) that k horses are the same colour and use this to
<BR>imply that k+1 horses are the same colour. Given the set of k+1 horses,
<BR>we remove one horse; then the remaining k horses are the same colour,
<BR>by hypothesis. We remove another horse and replace the first; the k
<BR>horses, by hypothesis, are again the same colour. We repeat this until
<BR>by exhaustion the k+1 sets of k horses have been shown to be the same
<BR>colour. It follows that since every horse is the same colour as every
<BR>other horse, P(k) entails P(k+1). But since we have shown P(1) to be
<BR>true, P is true for all succeeding values of k, that is, all horses are
<BR>the same colour.
<BR>
<BR>Theorem 1. Every horse has an infinite number of legs.
<BR>(Proof by intimidation.)
<BR>
<BR>Proof. Horses have an even number of legs. Behind they have two legs
<BR>and in front they have fore legs. This makes six legs, which is cer-
<BR>tainly an odd number of legs for a horse. But the only number that is
<BR>both odd and even is infinity. Therefore horses have an infinite num-
<BR>ber of legs. Now to show that this is general, suppose that somewhere
<BR>there is a horse with a finite number of legs. But that is a horse of
<BR>another colour, and by the lemma that does not exist.
<BR>
<BR>Corollary 1. Everything is the same colour.
<BR>
<BR>Proof. The proof of lemma 1 does not depend at all on the nature of the
<BR>object under consideration. The predicate of the antecedent of the uni-
<BR>versally-quantified conditional \'For all x, if x is a horse, then x is
<BR>the same colour,\' namely \'is a horse\' may be generalized to \'is anything\'
<BR>without affecting the validity of the proof; hence, \'for all x, if x is
<BR>anything, x is the same colour.\'
<BR>
<BR>Corollary 2. Everything is white.
<BR>
<BR>Proof. If a sentential formula in x is logically true, then any parti-
<BR>cular substitution instance of it is a true sentence. In particular
<BR>then: \'for all x, if x is an elephant, then x is the same colour\' is
<BR>true. Now it is manifestly axiomatic that white elephants exist (for
<BR>proof by blatant assertion consult Mark Twain \'The Stolen White Ele-
<BR>phant\'). Therefore all elephants are white. By corollary 1 everything
<BR>is white.
<BR>
<BR>Theorem 2. Alexander the Great did not exist and he had an infinite
<BR>number of limbs.
<BR>
<BR>Proof. We prove this theorem in two parts. First we note the obvious
<BR>fact that historians always tell the truth (for historians always take
<BR>a stand, and therefore they cannot lie). Hence we have the historically
<BR>true sentence, \'If Alexander the Great existed, then he rode a black
<BR>horse Bucephalus.\' But we know by corollary 2 everything is white;
<BR>hence Alexander could not have ridden a black horse. Since the conse-
<BR>quent of the conditional is false, in order for the whole statement to
<BR>be true the antecedent must be false. Hence Alexander the Great did not
<BR>exist.
<BR>We have also the historically true statement that Alexander was warned
<BR>by an oracle that he would meet death if he crossed a certain river. He
<BR>had two legs; and \'forewarned is four-armed.\' This gives him six limbs,
<BR>an even number, which is certainly an odd number of limbs for a man.
<BR>Now the only number which is even and odd is infinity; hence Alexander
<BR>had an infinite number of limbs. We have thus proved that Alexander the
<BR>Great did not exist and that he had an infinite number of limbs.
<BR>
<BR>
<BR>-----------
<BR>
<BR>Not precisely pure-math, but ...
<BR>
<BR>Fuller\'s Law of Cosmic Irreversability:
<BR>
<BR>1 pot T --> 1 pot P
<BR>but
<BR>1 pot P -/-> 1 pot T
<BR>
<BR>----------
<BR>A tribe of Native Americans generally referred to their woman by the
<BR>animal hide with which they made their blanket. Thus, one woman might
<BR>be known as Squaw of Buffalo Hide, while another might be known as
<BR>Squaw of Deer Hide. This tribe had a particularly large and strong
<BR>woman, with a very unique (for North America anyway) animal hide for
<BR>her blanket. This woman was known as Squaw of Hippopotamus hide, and
<BR>she was as large and powerful as the animal from which her blanket was
<BR>made.
<BR>
<BR>Year after year, this woman entered the tribal wrestling tournament,
<BR>and easily defeated all challengers; male or female. As the men of
<BR>the tribe admired her strength and power, this made many of the other
<BR>woman of the tribe extremely jealous. One year, two of the squaws
<BR>petitioned the Chief to allow them to enter their sons together as a
<BR>wrestling tandem in order to wrestle Squaw of the Hippopotamus hide as
<BR>a team. In this way, they hoped to see that she would no longer be
<BR>champion wrestler of the tribe.
<BR>
<BR>As the luck of the draw would have it, the two sons who were wrestling
<BR>as a tandem met the squaw in the final and championship round of the
<BR>wrestling contest. As the match began, it became clear that the squaw
<BR>had finally met an opponent that was her equal. The two sons wrestled
<BR>and struggled vigorously and were clearly on an equal footing with the
<BR>powerful squaw. Their match lasted for hours without a clear victor.
<BR>Finally the chief intervened and declared that, in the interests of
<BR>the health and safety of the wrestlers, the match was to be terminated
<BR>and that he would declare a winner.
<BR>
<BR>The chief retired to his teepee and contemplated the great struggle he
<BR>had witnessed, and found it extremely difficult to decide a winner.
<BR>While the two young men had clearly outmatched the squaw, he found it
<BR>difficult to force the squaw to relinquish her tribal championship.
<BR>After all, it had taken two young men to finally provide her with a
<BR>decent match. Finally, after much deliberation, the chief came out
<BR>from his teepee, and announced his decision. He said...
<BR>
<BR>\"The Squaw of the Hippopotamus hide is equal to the sons of the squaws
<BR>of the other two hides\"
<BR>
<BR>-----------
<BR>A topologist is a man who doesn\'t know the difference between a coffee
<BR>cup and a doughnut.
<BR>
<BR>-----------
<BR>A statistician can have his head in an oven and his feet in ice, and
<BR>he will say that on the average he feels fine.
<BR>
<BR>----------
<BR>A guy decided to go to the brain transplant clinic to refreshen his
<BR>supply of brains. The secretary informed him that they had three
<BR>kinds of brains available at that time. Doctors\' brains were going
<BR>for $20 per ounce and lawyers\' brains were getting $30 per ounce. And
<BR>then there were mathematicians\' brains which were currently fetching
<BR>$1000 per ounce.
<BR>
<BR>\"A 1000 dollars an ounce!\" he cried. \"Why are they so expensive?\"
<BR>
<BR>\"It takes more mathematicians to get an ounce of brains,\" she explained.
<BR>
<BR>-----------
<BR>A topologist walks into a bar and orders a drink. The bartender,
<BR>being a number theorist, says, \"I\'m sorry, but we don\'t serve
<BR>topologists here.\"
<BR>
<BR>The disgruntled topologist walks outside, but then gets an idea and
<BR>performs Dahn surgery upon herself. She walks into the bar, and the
<BR>bartender, who does not recognize her since she is now a different
<BR>manifold, serves her a drink. However, the bartender thinks she looks
<BR>familiar, or at least locally similar, and asks, \"Aren\'t you that
<BR>topologist that just came in here?\"
<BR>
<BR>To which she responds, \"No, I\'m a frayed knot.\"
<BR>
<BR>-----------
<BR>There are three kinds of people in the world;
<BR>those who can count and those who can\'t.
<BR>
<BR>And the related:
<BR>
<BR>There are two groups of people in the world;
<BR>those who believe that the world can be
<BR>divided into two groups of people,
<BR>and those who don\'t.
<BR>
<BR>And then:
<BR>
<BR>There are two groups of people in the world:
<BR>Those who can be categorized into one of two
<BR>groups of people, and those who can\'t.
<BR>
<BR>----------
<BR>
<BR>The world is divided into two classes:
<BR>people who say \"The world is divided into two classes\",
<BR>and people who say
<BR>The world is divided into two classes:
<BR>people who say: \"The world is divided into two classes\",
<BR>and people who say:
<BR>The world is divided into two classes:
<BR>people who say ...
<BR>
<BR>----------
<BR>What follows is a \"quiz\" a student of mine once showed me (which she\'d
<BR>gotten from a previous teacher, etc...). It\'s multiple choice, and if
<BR>you sort the letters (with upper and lower case disjoint) questions
<BR>and answers will come out next to each other. Enjoy...
<BR>
<BR>S. What the acorn said when he grew up
<BR>N. bisects
<BR>u. A dead parrot
<BR>g. center
<BR>F. What you should do when it rains
<BR>R. hypotenuse
<BR>m. A geometer who has been to the beach
<BR>H. coincide
<BR>h. The set of cards is missing
<BR>y. polygon
<BR>A. The boy has a speech defect
<BR>t. secant
<BR>K. How they schedule gym class
<BR>p. tangent
<BR>b. What he did when his mother-in-law wanted to go home
<BR>D. ellipse
<BR>O. The tall kettle boiling on the stove
<BR>W. geometry
<BR>r. Why the girl doesn\'t run a 4-minute mile
<BR>j. decagon
<BR>
<BR>-----------
<BR>___ 1. That which Noah built.
<BR>___ 2. An article for serving ice cream.
<BR>___ 3. What a bloodhound does in chasing a woman.
<BR>___ 4. An expression to represent the loss of a parrot.
<BR>___ 5. An appropriate title for a knight named Koal.
<BR>___ 6. A sunburned man.
<BR>___ 7. A tall coffee pot perking.
<BR>___ 8. What one does when it rains.
<BR>___ 9. A dog sitting in a refrigerator.
<BR>___ 10. What a boy does on the lake when his motor won\'t run.
<BR>___ 11. What you call a person who writes for an inn.
<BR>___ 12. What the captain said when the boat was bombed.
<BR>___ 13. What a little acorn says when he grows up.
<BR>___ 14. What one does to trees that are in the way.
<BR>___ 15. What you do if you have yarn and needles.
<BR>___ 16. Can George Washington turn into a country?
<BR>
<BR>
<BR>A. hypotenuse I. circle
<BR>B. polygon J. axiom
<BR>C. inscribe K. cone
<BR>D. geometry L. coincide
<BR>E. unit M. cosecant
<BR>F. center N. tangent
<BR>G. decagone O. hero
<BR>H. arc P. perpendicular
<BR>
<BR>----------
<BR>
<BR>A team of engineers were required to measure the height of a flag
<BR>pole. They only had a measuring tape, and were getting quite
<BR>frustrated trying to keep the tape along the pole. It kept falling
<BR>down, etc.
<BR>
<BR>A mathematician comes along, finds out their problem, and proceeds to
<BR>remove the pole from the ground and measure it easily.
<BR>
<BR>When he leaves, one engineer says to the other: \"Just like a
<BR>mathematician! We need to know the height, and he gives us the
<BR>length!\"
<BR>
<BR>-----------
<BR>A man camped in a national park, and noticed Mr. Snake and Mrs. Snake
<BR>slithering by. \"Where are all the little snakes?\" he asked. Mr.
<BR>Snake replied, \"We are adders, so we cannot multiply.\"
<BR>
<BR>The following year, the man returned to the same camping spot. This
<BR>time there were a whole batch of little snakes. \"I thought you said
<BR>you could not multiply,\" he said to Mr. Snake. \"Well, the park ranger
<BR>came by and built a log table, so now we can multiply by adding!\"
<BR>
<BR>----------
<BR>Einstein dies and goes to heaven only to be informed that his room is
<BR>not yet ready. \"I hope you will not mind waiting in a dormitory. We
<BR>are very sorry, but it\'s the best we can do and you will have to share
<BR>the room with others.\" he is told by the doorman (say his name is
<BR>Pete). Einstein says that this is no problem at all and that there is
<BR>no need to make such a great fuss. So Pete leads him to the dorm.
<BR>They enter and Albert is introduced to all of the present
<BR>inhabitants. \"See, Here is your first room mate. He has an IQ of
<BR>180!\"
<BR>\"Why that\'s wonderful!\" Says Albert. \"We can discuss mathematics!\"
<BR>\"And here is your second room mate. His IQ is 150!\"
<BR>\"Why that\'s wonderful!\" Says Albert. \"We can discuss physics!\"
<BR>\"And here is your third room mate. His IQ is 100!\"
<BR>\"That Wonderful! We can discuss the latest plays at the theater!\"
<BR>Just then another man moves out to capture Albert\'s hand and shake it.
<BR>\"I\'m your last room mate and I\'m sorry, but my IQ is only 80.\"
<BR>Albert smiles back at him and says, \"So, where do you think interest
<BR>rates are headed?\"
<BR>
<BR>----------
<BR>97.3% of all statistics are made up.
<BR>
<BR>-----------
<BR>Did you hear the one about the statistician?
<BR>
<BR>Probably....
<BR>
<BR>-----------
<BR>There was once a very smart horse. Anything that was shown it, it
<BR>mastered easily, until one day, its teachers tried to teach it about
<BR>rectangular coordinates and it couldn\'t understand them. All the
<BR>horse\'s acquaintances and friends tried to figure out what was the
<BR>matter and couldn\'t. Then a new guy (what the heck, a computer
<BR>engineer) looked at the problem and said,
<BR>
<BR>\"Of course he can\'t do it. Why, you\'re putting Descartes before the
<BR>horse!\"
<BR>
<BR>-----------
<BR>TOP TEN EXCUSES FOR NOT DOING THE MATH HOMEWORK
<BR>
<BR>1. I accidentally divided by zero and my paper burst into flames.
<BR>2. Isaac Newton\'s birthday.
<BR>3. I could only get arbitrarily close to my textbook. I couldn\'t
<BR>actually reach it.
<BR>4. I have the proof, but there isn\'t room to write it in this margin.
<BR>5. I was watching the World Series and got tied up trying to prove
<BR>that it converged.
<BR>6. I have a solar powered calculator and it was cloudy.
<BR>7. I locked the paper in my trunk but a four-dimensional dog got in
<BR>and ate it.
<BR>8. I couldn\'t figure out whether i am the square of negative one or
<BR>i is the square root of negative one.
<BR>9. I took time out to snack on a doughnut and a cup of coffee.
<BR>I spent the rest of the night trying to figure which one to dunk.
<BR>10. I could have sworn I put the homework inside a Klein bottle, but
<BR>this morning I couldn\'t find it.
<BR>
<BR>-----------
<BR>The guy gets on a bus and starts threatening everybody: \"I\'ll integrate
<BR>you! I\'ll differentiate you!!!\" So everybody gets scared and runs
<BR>away. Only one person stays. The guy comes up to him and says:
<BR>\"Aren\'t you scared, I\'ll integrate you, I\'ll differentiate you!!!\" And
<BR>the other guy says; \"No, I am not scared, I am e to the x.\"
<BR>
<BR>-----------
<BR>A mathematician went insane and believed that he was the
<BR>differentiation operator. His friends had him placed in a mental
<BR>hospital until he got better. All day he would go around frightening
<BR>the other patients by staring at them and saying \"I differentiate
<BR>you!\"
<BR>
<BR>One day he met a new patient; and true to form he stared at him and
<BR>said \"I differentiate you!\", but for once, his victim\'s expression
<BR>didn\'t change. Surprised, the mathematician marshalled his energies,
<BR>stared fiercely at the new patient and said loudly \"I differentiate
<BR>you!\", but still the other man had no reaction. Finally, in
<BR>frustration, the mathematician screamed out \"I DIFFERENTIATE YOU!\" --
<BR>at which point the new patient calmly looked up and said, \"You can
<BR>differentiate me all you like: I\'m e to the x.\"
<BR>
<BR>----------
<BR>/
<BR>| 1
<BR>| ----- = log cabin
<BR>| cabin
<BR>/
<BR>
<BR>Oops, you forgot your constant of integration.
<BR>
<BR>
<BR>/
<BR>| 1
<BR>| ----- = log cabin + C
<BR>| cabin
<BR>/
<BR>
<BR>And, as we all know,
<BR>
<BR>log cabin + C = houseboat
<BR>
<BR>----------
<BR>8 5
<BR>If lim - = oo (infinity), then what does lim - = ?
<BR>x->0 x x->0 x
<BR>
<BR>answer: (write 5 on it\'s side)
<BR>
<BR>----------
<BR>Why did the cat fall off the roof?
<BR>
<BR>Because he lost his mu. (mew=sound cats make, mu=coeff of friction)
<BR>
<BR>----------
<BR>Boy\'s Life, May 1973:
<BR>
<BR>Ralph: Dad, will you do my math for me tonight?
<BR>Dad: No, son, it wouldn\'t be right.
<BR>Ralph: Well, you could try.
<BR>
<BR>----------
<BR>Mrs. Johnson the elementary school math teacher was having children do
<BR>problems on the blackboard that day.
<BR>
<BR>``Who would like to do the first problem, addition?\'\'
<BR>
<BR>No one raised their hand. She called on Tommy, and with some help he
<BR>finally got it right.
<BR>
<BR>``Who would like to do the second problem, subtraction?\'\'
<BR>
<BR>Students hid their faces. She called on Mark, who got the problem but
<BR>there was some suspicion his girlfriend Lisa whispered it to him.
<BR>
<BR>``Who would like to do the third problem, division?\'\'
<BR>
<BR>Now a low collective groan could be heard as everyone looked at
<BR>nothing in particular. The teacher called on Suzy, who got it right
<BR>(she has been known to hold back sometimes in front of her friends).
<BR>
<BR>``Who would like to do the last problem, multiplication?\'\'
<BR>
<BR>Tim\'s hand shot up, surprising everyone in the room. Mrs. Johnson
<BR>finally gained her composure in the stunned silence. ``Why the
<BR>enthusiasm, Tim?\'\'
<BR>
<BR>``God said to go fourth and multiply!\'\'
<BR>
<BR>-----------
<BR>Definitions of Terms Commonly Used in Higher Math
<BR>
<BR>The following is a guide to the weary student of mathematics who
<BR>is often confronted with terms which are commonly used but rarely
<BR>defined. In the search for proper definitions for these terms we
<BR>found no authoritative, nor even recognized, source. Thus, we
<BR>followed the advice of mathematicians handed down from time
<BR>immortal: \"Wing It.\"
<BR>
<BR>
<BR>CLEARLY: I don\'t want to write down all the \"in-
<BR>between\" steps.
<BR>
<BR>TRIVIAL: If I have to show you how to do this, you\'re
<BR>in the wrong class.
<BR>
<BR>OBVIOUSLY: I hope you weren\'t sleeping when we discussed
<BR>this earlier, because I refuse to repeat it.
<BR>
<BR>RECALL: I shouldn\'t have to tell you this, but for
<BR>those of you who erase your memory tapes
<BR>after every test...
<BR>
<BR>WLOG (Without Loss Of Generality): I\'m not about to do all the
<BR>possible cases, so I\'ll do one and let you
<BR>figure out the rest.
<BR>
<BR>IT CAN EASILY BE SHOWN: Even you, in your finite wisdom, should
<BR>be able to prove this without me holding your
<BR>hand.
<BR>
<BR>CHECK or CHECK FOR YOURSELF: This is the boring part of the
<BR>proof, so you can do it on your own time.
<BR>
<BR>SKETCH OF A PROOF: I couldn\'t verify all the details, so I\'ll
<BR>break it down into the parts I couldn\'t
<BR>prove.
<BR>
<BR>HINT: The hardest of several possible ways to do a
<BR>proof.
<BR>
<BR>BRUTE FORCE (AND IGNORANCE): Four special cases, three counting
<BR>arguments, two long inductions, \"and a
<BR>partridge in a pair tree.\"
<BR>
<BR>SOFT PROOF: One third less filling (of the page) than
<BR>your regular proof, but it requires two extra
<BR>years of course work just to understand the
<BR>terms.
<BR>
<BR>ELEGANT PROOF: Requires no previous knowledge of the subject
<BR>matter and is less than ten lines long.
<BR>
<BR>SIMILARLY: At least one line of the proof of this case is
<BR>the same as before.
<BR>
<BR>CANONICAL FORM: 4 out of 5 mathematicians surveyed
<BR>recommended this as the final form for their
<BR>students who choose to finish.
<BR>
<BR>TFAE (The Following Are Equivalent): If I say this it means that,
<BR>and if I say that it means the other thing,
<BR>and if I say the other thing...
<BR>
<BR>BY A PREVIOUS THEOREM: I don\'t remember how it goes (come to
<BR>think of it I\'m not really sure we did this
<BR>at all), but if I stated it right (or at
<BR>all), then the rest of this follows.
<BR>
<BR>TWO LINE PROOF: I\'ll leave out everything but the conclusion,
<BR>you can\'t question \'em if you can\'t see \'em.
<BR>
<BR>BRIEFLY: I\'m running out of time, so I\'ll just write
<BR>and talk faster.
<BR>
<BR>LET\'S TALK THROUGH IT: I don\'t want to write it on the board lest
<BR>I make a mistake.
<BR>
<BR>PROCEED FORMALLY: Manipulate symbols by the rules without any
<BR>hint of their true meaning (popular in pure
<BR>math courses).
<BR>
<BR>QUANTIFY: I can\'t find anything wrong with your proof
<BR>except that it won\'t work if x is a moon of
<BR>Jupiter (Popular in applied math courses).
<BR>
<BR>PROOF OMITTED: Trust me, It\'s true.
<BR>
<BR>[ Questo Messaggio è stato Modificato da: livingbooks il 04-04-2004 12:07 ]<BR><BR>[ Questo Messaggio è stato Modificato da: livingbooks il 04-04-2004 12:11 ]

<DIV style=\"font-size:1pt;font-family:arial\">
<BR>-------------------------------------------------------------------------------
<BR>In the bayous of Louisiana, there is a small river called the Dirac.
<BR>Many wealthy people have their mansions near its mouth. One of the
<BR>social leaders decided to have a grand ball. Being a cousin of the
<BR>Governor, she arranged for a detachment of the state militia to serve
<BR>as guards and traffic directors for the big doings. A captain was
<BR>sent over with a small company; naturally he asked if there was enough
<BR>room for him and his unit. The social leader replied, \"But of course,
<BR>Captain! It is well known that the Dirac delta function has unit
<BR>area.\"
<BR>
<BR>-------------------------------------------------------------------------------
<BR>Albert Einstein, who fancied himself as a violinist, was rehearsing a
<BR>Haydn string quartet. When he failed for the fourth time to get his
<BR>entry in the second movement, the cellist looked up and said, \"The
<BR>problem with you, Albert, is that you simply can\'t count.\"
<BR>
<BR>------------------------------------------------------------------------------
<BR>Some famous mathematician was to give a keynote speech at a
<BR>conference. Asked for an advance summary, he said he would present a
<BR>proof of Fermat\'s Last Theorem -- but they should keep it under their
<BR>hats. When he arrived, though, he spoke on a much more prosaic
<BR>topic. Afterwards the conference organizers asked why he said he\'d
<BR>talk about the theorem and then didn\'t. He replied this was his
<BR>standard practice, just in case he was killed on the way to the
<BR>conference.
<BR>
<BR>-------------------------------------------------------------------------------
<BR>When I was a Math/Chem grad student at Princeton in 1973-74, there was
<BR>a story going around about a grad student. This guy was always late.
<BR>One day he stumbled into class late, saw seven problems written on the
<BR>board, and wrote them down. As the week went on he began to panic:
<BR>the math department at Princeton is fiercely competitive, and here he
<BR>was unable to do most of a simple homework assignment! When the next
<BR>class rolled around he only had solved two of the problems, although
<BR>he had a pretty good idea of how to solve a third but not enough time
<BR>to complete it.
<BR>
<BR>When he dejectedly flung his partial assignment on the prof\'s desk,
<BR>the prof asked him \"What\'s that?\" \"The homework.\" \"What homework?\"
<BR>Eventually it came out that what the prof had written on the board
<BR>were the seven most important unsolved problems in the field.
<BR>
<BR>This is largely an academic legend, at least according to Jan Harold
<BR>Brunvand, the author of a series of books on so-called Urban Legends.
<BR>He talks about it in his latest book _Curses! Broiled Again!_ in the
<BR>chapter entitled \"The Unsolvable Math Problem.\" It is, however, based
<BR>in some fact. The Stanford mathematician, George B. Danzig,
<BR>apparently managed to solve two statistics problems previously
<BR>unsolved under similar circumstances.
<BR>
<BR>-------------------------------------------------------------------------------
<BR>The following problem can be solved either the easy way or the hard way.
<BR>
<BR>Two trains 200 miles apart are moving toward each other; each one is
<BR>going at a speed of 50 miles per hour. A fly starting on the front of
<BR>one of them flies back and forth between them at a rate of 75 miles
<BR>per hour. It does this until the trains collide and crush the fly to
<BR>death. What is the total distance the fly has flown?
<BR>
<BR>The fly actually hits each train an infinite number of times before it
<BR>gets crushed, and one could solve the problem the hard way with pencil
<BR>and paper by summing an infinite series of distances. The easy way
<BR>is as follows: Since the trains are 200 miles apart and each train is
<BR>going 50 miles an hour, it takes 2 hours for the trains to collide.
<BR>Therefore the fly was flying for two hours. Since the fly was flying
<BR>at a rate of 75 miles per hour, the fly must have flown 150 miles.
<BR>That\'s all there is to it.
<BR>
<BR>When this problem was posed to John von Neumann, he immediately
<BR>replied, \"150 miles.\"
<BR>
<BR>\"It is very strange,\" said the poser, \"but nearly everyone tries to
<BR>sum the infinite series.\"
<BR>
<BR>\"What do you mean, strange?\" asked Von Neumann. \"That\'s how I did it!\"
<BR>
<BR>-------------------------------------------------------------------------------
<BR>Mathematicians are like Frenchmen: whatever you say to them, they
<BR>translate it into their own language, and forthwith it means something
<BR>entirely different.
<BR>-- Johann Wolfgang von Goethe
<BR>
<BR>-------------------------------------------------------------------------------
<BR>\"The reason that every major university maintains a department of
<BR>mathematics is that it is cheaper to do this than to institutionalize
<BR>all those people.\"
<BR>
<BR>-------------------------------------------------------------------------------
<BR>Three mathematicians and a physicist walk into a bar.
<BR>You\'d think the second one would have ducked. (Ha, that quack\'s me up!)
<BR>
<BR>-------------------------------------------------------------------------------
<BR>What do you call a young eigensheep?
<BR>
<BR>A lamb, duh!!!
<BR>
<BR>-------------------------------------------------------------------------------
<BR>\"The world is everywhere dense with idiots.\"
<BR>- LFS
<BR>
<BR>-------------------------------------------------------------------------------
<BR>One day a farmer called up an engineer, a physicist, and a mathematician
<BR>and asked them to fence of the largest possible area with the least
<BR>amount of fence. The engineer made the fence in a circle and
<BR>proclaimed that he had the most efficient design. The physicist made
<BR>a long, straight line and proclaimed \'We can assume the length is
<BR>infinite...\' and pointed out that fencing off half of the Earth was
<BR>certainly a more efficient way to do it. The Mathematician just
<BR>laughed at them. He built a tiny fence around himself and said \'I
<BR>declare myself to be on the outside.\'
<BR>
<BR>-------------------------------------------------------------------------------
<BR>An engineer, a mathematician, and a computer programmer are driving
<BR>down the road when the car they are in gets a flat tire. The engineer
<BR>says that they should buy a new car. The mathematician says they
<BR>should sell the old tire and buy a new one. The computer programmer
<BR>says they should drive the car around the block and see if the tire
<BR>fixes itself.
<BR>
<BR>------------------------------------------------------------------------------
<BR>A math/computer science convention was being held. On the train to
<BR>the convention, a bunch of math majors and a bunch of computer science
<BR>majors were on the train. Each of the math majors had his/her train
<BR>ticket. The group of computer science majors had only ONE ticket for
<BR>all of them. The math majors started laughing and snickering.
<BR>
<BR>Then, one of the CS majors said \"here comes the conductor\" and then
<BR>all of the CS majors went into the bathroom. The math majors were
<BR>puzzled. The conductor came aboard and said \"tickets please\" and got
<BR>tickets from all the math majors. He then went to the bathroom and
<BR>knocked on the door and said \"ticket please\" and the CS majors stuck
<BR>the ticket under the door. The conductor took it and then the CS
<BR>majors came out of the bathroom a few minutes later. The math majors
<BR>felt really stupid.
<BR>
<BR>So, on the way back from the convention, the group of math majors had
<BR>one ticket for the group. They started snickering at the CS majors,
<BR>for the whole group had no tickets amongst them. Then, the CS major
<BR>lookout said \"Conductor coming!\". All the CS majors went to the
<BR>bathroom. All the math majors went to another bathroom. Then, before
<BR>the conductor came on board, one of the CS majors left the bathroom,
<BR>knocked on the other bathroom, and said \"ticket please.\"
<BR>
<BR>------------------------------------------------------------------------------
<BR>The following is supposedly a true story about Russell. It isn\'t
<BR>really a math joke since it makes fun of the British hierarchy, but
<BR>it\'s funny anyway....
<BR>
<BR>Around the time when Cold War started, Bertrand Russell was giving a
<BR>lecture on politics in England. Being a leftist in a conservative
<BR>women\'s club, he was not received well at all: the ladies came up to
<BR>him and started attacking him with whatever they could get their hands
<BR>on. The guard, being an English gentleman, did not want to be rough
<BR>to the ladies and yet needed to save Russell from them. He said, \"But
<BR>he is a great mathematician!\" The ladies ignored him. The guard said
<BR>again, \"But he is a great philosopher!\" The ladies ignore him again.
<BR>In desperation, finally, he said, \"But his brother is an earl!\" Bert
<BR>was saved.
<BR>
<BR>------------------------------------------------------------------------------
<BR>Another \"true\" story, kinda like the aforementioned urban legend:
<BR>
<BR>Enrico Fermi, while studying in college, was bored by his math
<BR>classes. He walked up to the professor and said, \"My classes are too
<BR>easy!\" The professor looked at him, and said, \"Well, I\'m sure you\'ll
<BR>find this interesting.\" Then the professor copied 9 problems from a
<BR>book to a paper and gave the paper to Fermi. A month later, the
<BR>professor ran into Fermi, \"So how are you doing with the problems I
<BR>gave you?\" \"Oh, they are very hard. I only managed to solve 6 of
<BR>them.\" The professor was visibly shocked, \"What!? But those are
<BR>unsolved problems!\"
<BR>
<BR>-------------------------------------------------------------------------------
<BR>An engineer, a physicist, and a mathematician find themselves in an
<BR>anecdote, indeed an anecdote quite similar to many that you have no
<BR>doubt already heard. After some observations and rough calculations,
<BR>the engineer realizes the situation and starts laughing. A few
<BR>minutes later the physicist understands, too, and chuckles to himself
<BR>happily as he now has enough experimental evidence to publish a paper.
<BR>This leaves the mathematician somewhat perplexed, as he had observed
<BR>right away that he was the subject of an anecdote, and deduced quite
<BR>rapidly the presence of humour from similar anecdotes, but considers
<BR>this anecdote to be too trivial a corollary to be significant, let
<BR>alone funny.
<BR>
<BR>
<BR>-------------------------------------------------------------------------------
<BR>\"A person who can, within a year, solve x^2 - 92y^2 = 1 is a mathematician.\"
<BR>-- Brahmagupta
<BR>
<BR>-------------------------------------------------------------------------------
<BR>Math and Alcohol don\'t mix, so...
<BR>
<BR>PLEASE DON\'T DRINK AND DERIVE
<BR>
<BR>Then there\'s every parent\'s scream when their child walks into the
<BR>room dazed and staggering:
<BR>
<BR>OH NO...YOU\'VE BEEN TAKING DERIVATIVES!!
<BR>
<BR>-------------------------------------------------------------------------------
<BR>MADD = Mathematicians
<BR>Against
<BR>Drunk
<BR>Deriving
<BR>
<BR>-------------------------------------------------------------------------------
<BR>[This limerick was previously posted incorrectly.
<BR>The integral limit has been changed.]
<BR>
<BR>Here\'s a limerick I picked up off the net a few years back - looks better
<BR>on paper.
<BR>
<BR>3_
<BR>\\/3
<BR>/
<BR>| 2 3 X pi 3_
<BR>| z dz X cos(--------) = ln (\\/e )
<BR>| 9
<BR>/
<BR>1
<BR>
<BR>Which, of course, translates to:
<BR>
<BR>Integral z-squared dz
<BR>from 1 to the cube root of 3
<BR>times the cosine
<BR>of three pi over 9
<BR>equals log of the cube root of \'e\'.
<BR>
<BR>And it\'s correct, too.
<BR>
<BR>-------------------------------------------------------------------------------
<BR>This poem was written by John Saxon (an author of math textbooks).
<BR>
<BR>((12 + 144 + 20 + (3 * 4^(1/2))) / 7) + (5 * 11) = 9^2 + 0
<BR>
<BR>
<BR>Or for those who have trouble with the poem:
<BR>
<BR>A Dozen, a Gross and a Score,
<BR>plus three times the square root of four,
<BR>divided by seven,
<BR>plus five times eleven,
<BR>equals nine squared and not a bit more.
<BR>
<BR>-------------------------------------------------------------------------------
<BR>\'Tis a favorite project of mine
<BR>A new value of pi to assign.
<BR>I would fix it at 3
<BR>For it\'s simpler, you see,
<BR>Than 3 point 1 4 1 5 9.
<BR>
<BR>(\"The Lure of the Limerick\" by W.S. Baring-Gould, p.5. Attributed to
<BR>Harvey L. Carter).
<BR>
<BR>-------------------------------------------------------------------------------
<BR>If inside a circle a line
<BR>Hits the center and goes spine to spine
<BR>And the line\'s length is \"d\"
<BR>the circumference will be
<BR>d times 3.14159
<BR>
<BR>-------------------------------------------------------------------------------
<BR>
<BR>If (1+x) (real close to 1)
<BR>Is raised to the power of 1
<BR>Over x, you will find
<BR>Here\'s the value defined:
<BR>2.718281...
<BR>
<BR>-------------------------------------------------------------------------------
<BR>An engineer thinks that his equations are an approximation to reality.
<BR>A physicist thinks reality is an approximation to his equations.
<BR>A mathematician doesn\'t care.
<BR>
<BR>-------------------------------------------------------------------------------
<BR>Why is the number 10 afraid of seven?
<BR>
<BR>-- because seven ate nine.
<BR>
<BR>-------------------------------------------------------------------------------
<BR>We use epsilons and deltas in mathematics because mathematicians tend
<BR>to make errors.
<BR>
<BR>------------------------------------------------------------------------------
<BR>
<BR>What\'s big, grey, and proves the uncountability of the reals?
<BR>Cantor\'s Diagonal Elephant!
<BR>
<BR>How can you tell that Harvard was layed out by a mathematician?
<BR>The div school [divinity school] is right next to the grad school...
<BR>
<BR>-------------------------------------------------------------------------------
<BR>The Stanford Linear Accelerator Center was known as SLAC, until the
<BR>big earthquake, when it became known as SPLAC.
<BR>
<BR>SPLAC? Stanford Piecewise Linear Accelerator.
<BR>
<BR>-------------------------------------------------------------------------------
<BR>Q: How many topologists does it take to change a light bulb?
<BR>A: It really doesn\'t matter, since they\'d rather knot.
<BR>
<BR>------------------------------------------------------------------------------
<BR>
<BR>A mathematician decides he wants to learn more about practical
<BR>problems. He sees a seminar with a nice title: \"The Theory of Gears.\"
<BR>So he goes. The speaker stands up and begins, \"The theory of gears
<BR>with a real number of teeth is well known ...\"
<BR>
<BR>-------------------------------------------------------------------------------
<BR>A group of scientists were doing an investigation into problem-solving
<BR>techniques, and constructed an experiment involving a physicist, an
<BR>engineer, and a mathematician.
<BR>
<BR>The experimental apparatus consisted of a water spigot and two identical
<BR>pails, one of which was fastened to the ground ten feet from the spigot.
<BR>
<BR>Each of the subjects was given the second pail, empty, and told to fill the
<BR>pail on the ground.
<BR>
<BR>The physicist was the first subject: he carried his pail to the spigot,
<BR>filled it there, carried it full of water to the pail on the ground, and
<BR>poured the water into it. Standing back, he declared, \"There: I have
<BR>solved the problem.\"
<BR>
<BR>The engineer and the mathematician each approached the problem similarly.
<BR>Upon finishing, the engineer noted that the solution was exact, since the
<BR>volumes of the pails were equal. The mathematician merely noted that he
<BR>had proven that a solution exists.
<BR>
<BR>Now, the experimenters altered the parameters of the task a bit: the pail
<BR>on the ground was still empty, but the subjects were presented with a pail
<BR>that was already half-filled with water.
<BR>
<BR>The physicist immediately carried his pail over to the one on the ground,
<BR>emptied the water into it, went back to the spigot, *filled* the pail, and
<BR>finally emptied the entire contents into the pail on the ground,
<BR>overflowing it and spilling some of the water. Upon finishing, he
<BR>commented that the problem should have been better stated.
<BR>
<BR>The engineer, in turn, thought for some time before going into action. He
<BR>then took his half-filled pail to the spigot, filled it to the brim, and
<BR>filled the pail on the ground from it. Again he noted that the problem had
<BR>an exact solution, which of course he had found.
<BR>
<BR>The mathematician thought for a long time before stirring. At last he
<BR>stood up, emptied his pail onto the ground, and declared, \"The problem has
<BR>been reduced to one already solved.\"
<BR>
<BR>-------------------------------------------------------------------------------
<BR>Professor Dirac, a famous Applied Mathematician-Physicist, had a horse
<BR>shoe over his desk. One day a student asked if he really believed
<BR>that a horse shoe brought luck. Professor Dirac replied, \"I
<BR>understand that it brings you luck if you believe in it or not.\"
<BR>
<BR>-------------------------------------------------------------------------------
<BR>First of all let me make it clear that I have nothing against
<BR>contravariant functors. Some of my best friends are cohomology
<BR>theories! But now you aren\'t supposed to call them contravariant
<BR>anymore. It\'s Algebraically Correct to call them \'differently
<BR>arrowed\'!!
<BR>
<BR>In the same way that transcendental numbers are polynomially
<BR>challenged?
<BR>
<BR>Manifolds are personifolds (humanifolds).
<BR>
<BR>Neighborhoods are neighbor victims of society.
<BR>
<BR>It\'s the Asian Remainder Theorem.
<BR>
<BR>It isn\'t PC to use \"singularity\" - the function is \"convergently
<BR>challenged\" there.
<BR>
<BR>-------------------------------------------------------------------------------
<BR>Why did the computer scientist die in the shower?
<BR>Because he read the instructions on the shampoo bottle, \"Lather,
<BR>rinse, repeat.\"
<BR>
<BR>Why did the calculus student have so much trouble making Kool-Aid?
<BR>Because he couldn\'t figure out how to get a quart of water into the
<BR>little package.
<BR>
<BR>Q: Why do computer scientists confuse Christmas and Halloween?
<BR>A: Because Oct 31 = Dec 25
<BR>
<BR>-------------------------------------------------------------------------------
<BR>Here are some phrases used to remember SIN, COS, and TAN.
<BR>(SIN = Opposite/Hypotenuse, COS = Adjacent/H, TAN = O/A).
<BR>
<BR>1. SOHCAHTOA (sock-a-toe-a)
<BR>
<BR>2. The Cat Sat
<BR>On An Orange
<BR>And Howled Hard
<BR>
<BR>3. Some Old Hulks
<BR>Carry A Huge
<BR>Tub Of Ale
<BR>
<BR>4. Silly Old Hitler
<BR>Caused Awful Headaches
<BR>To Our Airmen
<BR>
<BR>5. Some Old Hag
<BR>Cracked All Her
<BR>Teeth On Asparagus
<BR>
<BR>6. Some Old Hairy
<BR>Camels Are Hairier
<BR>Than Others Are
<BR>
<BR>7. Silly Old Harry
<BR>Caught A Herring
<BR>Trawling Off America
<BR>
<BR>8. SOPHY, CADHY, TOAD
<BR>
<BR>--------------------------------units and dimensions-------------
<BR>
<BR>2 monograms 1 diagram
<BR>8 nickles 2 paradigms
<BR>2 wharves 1 paradox
<BR>
<BR>10E5 bicycles 2 megacycles
<BR>
<BR>1 unit of suspense in an Agatha Christie novel 1 whod unit
<BR>
<BR>-------------------------------------------------------------------------------
<BR>Three Laws of Thermodynamics (paraphrased):
<BR>
<BR>First Law: You can\'t get anything without working for it.
<BR>
<BR>Second Law: The most you can accomplish by work is to break even.
<BR>
<BR>Third Law: You can\'t break even.
<BR>
<BR>-------------------------------------------------------------------------------
<BR>Q: What goes \"Pieces of seven! Pieces of seven!\"?
<BR>A: A parroty error!!
<BR>
<BR>Q: What did the circle say to the tangent line?
<BR>A: \"Stop touching me!\"
<BR>
<BR>-------------------------------------------------------------------------------
<BR>A mathematician is a person who says that, when 3 people are supposed
<BR>to be in a room but 5 came out, 2 have to go in so the room gets
<BR>empty...
<BR>
<BR>-------------------------------------------------------------------------------
<BR>The upgrade path to the most powerful and satisfying computer:
<BR>
<BR>* Pocket calculator
<BR>
<BR>* Commodore Pet / Apple II / TRS 80 / Commodore 64 / Timex Sinclair
<BR>(Choose any of the above)
<BR>
<BR>* IBM PC
<BR>
<BR>* Apple Macintosh
<BR>
<BR>* Fastest workstation of the time (HP, DEC, IBM, SGI: your choice)
<BR>
<BR>* Minicomputer (HP, DEC, IBM, SGI: your choice)
<BR>
<BR>* Mainframe (IBM, Cray, DEC: your choice)
<BR>
<BR>
<BR>And then you reach the pinnacle of modern computing facilities:
<BR>
<BR>*********************************************************
<BR>******* G R A D U A T E S T U D E N T S ********
<BR>*********************************************************
<BR>
<BR>Yes, you just sit back and do all of your computing through lowly
<BR>graduate students. Imagine the advantages:
<BR>
<BR>* Multi-processing, with as many processes as you have
<BR>students. You can easily add more power by promising more
<BR>desperate undergrads that they can indeed escape college
<BR>through your guidance. Special student units can even
<BR>handle several tasks *on*their*own*!
<BR>
<BR>* Full voice recognition interface. Never touch a keyboard or
<BR>mouse again. Just mumble commands and they *will* be
<BR>understood (or else!).
<BR>
<BR>* No hardware upgrades and no installation required. Every
<BR>student comes complete with all hardware necessary. Never
<BR>again fry a chip or $10,000 board by improper installation!
<BR>Just sit that sniveling student at a desk, give it writing
<BR>utensils (making sure to point out which is the dangerous
<BR>end) and off it goes.
<BR>
<BR>* Low maintenance. Remember when that hard disk crashed in
<BR>your Beta 9900, causing all of your work to go the great bit
<BR>bucket in the sky? This won\'t happen with grad. students.
<BR>All that is required is that you give them a good *whack!*
<BR>upside the head when they are acting up, and they will run
<BR>good as new.
<BR>
<BR>* Abuse module. Imagine yelling expletives at your computer.
<BR>Doesn\'t work too well, because your machine just sits there
<BR>and ignores you. Through the grad student abuse module you
<BR>can put the fear of god in them, and get results to boot!
<BR>
<BR>* Built-in lifetime. Remember that awful feeling two years
<BR>after you bought your GigaPlutz mainframe when the new
<BR>faculty member on the block sneered at you because his
<BR>FeelyWup workstation could compute rings around your
<BR>dinosaur? This doesn\'t happen with grad. students. When
<BR>they start wearing and losing productivity, simply give them
<BR>the PhD and boot them out onto the street to fend for
<BR>themselves. Out of sight, out of mind!
<BR>
<BR>* Cheap fuel: students run on Coca Cola (or the high-octane
<BR>equivalent -- Jolt Cola) and typically consume hot spicy
<BR>chinese dishes, cheap taco substitutes, or completely
<BR>synthetic macaroni replacements. It is entirely unnecessary
<BR>to plug the student into the wall socket (although this does
<BR>get them going a little faster from time to time).
<BR>
<BR>* Expansion options. If your grad. students don\'t seem to be
<BR>performing too well, consider adding a handy system manager
<BR>or software engineer upgrade. These guys are guaranteed to
<BR>require even less than a student, and typically establish
<BR>permanent residence in the computer room. You\'ll never know
<BR>they are around! (Which you certainly can\'t say for an
<BR>AXZ3000-69 150gigahertz space-heater sitting on your desk
<BR>with its ten noisy fans....) [Note however that the
<BR>engineering department still hasn\'t worked out some of the
<BR>idiosyncratic bugs in these expansion options, such as
<BR>incessant muttering at nobody in particular, occasionaly
<BR>screaming at your grad. students, and posting ridiculous
<BR>messages on world-wide bulletin boards.]
<BR>
<BR>So forget your Babbage Engines and abacuses (abaci?) and PortaBooks
<BR>and DEK 666-3D\'s and all that other silicon garbage. The wave of the
<BR>future is in wetware, so invest in graduate students today! You\'ll never
<BR>go back!
<BR>
<BR>-------------------------------------------------------------------------------
<BR>If I have seen farther than others, it is because I was
<BR>standing on the shoulder of giants.
<BR>-- Isaac Newton
<BR>
<BR>If I have not seen as far as others, it is because giants
<BR>were standing on my shoulders.
<BR>-- Hal Abelson
<BR>
<BR>In computer science, we stand on each other\'s feet.
<BR>-- Brian K. Reid
<BR>
<BR>-------------------------------------------------------------------------------
<BR>He thinks he\'s really smooth, but he\'s only C^1.
<BR>He\'s always going off on a tangent.
<BR>
<BR>-------------------------------------------------------------------------------
<BR>A mathematician and a physicist agree to a psychological experiment.
<BR>The mathematician is put in a chair in a large empty room and a
<BR>beautiful naked woman is placed on a bed at the other end of the room.
<BR>The psychologist explains, \"You are to remain in your chair. Every
<BR>five minutes, I will move your chair to a position halfway between its
<BR>current location and the woman on the bed.\" The mathematician looks
<BR>at the psychologist in disgust. \"What? I\'m not going to go through
<BR>this. You know I\'ll never reach the bed!\" And he gets up and storms
<BR>out. The psychologist makes a note on his clipboard and ushers the
<BR>physicist in. He explains the situation, and the physicist\'s eyes
<BR>light up and he starts drooling. The psychologist is a bit confused.
<BR>\"Don\'t you realize that you\'ll never reach her?\" The physicist smiles
<BR>and replied, \"Of course! But I\'ll get close enough for all practical
<BR>purposes!\"
<BR>
<BR>-------------------------------------------------------------------------------
<BR>Dean, to the physics department. \"Why do I always have to give you
<BR>guys so much money, for laboratories and expensive equipment and
<BR>stuff. Why couldn\'t you be like the math department - all they need
<BR>is money for pencils, paper and waste-paper baskets. Or even better,
<BR>like the philosophy department. All they need are pencils and paper.\"
<BR>
<BR>-------------------------------------------------------------------------------
<BR>An engineer, physicist, and mathematician are all challenged with a
<BR>problem: to fry an egg when there is a fire in the house. The
<BR>engineer just grabs a huge bucket of water, runs over to the fire, and
<BR>puts it out. The physicist thinks for a long while, and then measures
<BR>a precise amount of water into a container. He takes it over to the
<BR>fire, pours it on, and with the last drop the fire goes out. The
<BR>mathematician pores over pencil and paper. After a few minutes he
<BR>goes \"Aha! A solution exists!\" and goes back to frying the egg.
<BR>
<BR>Sequel: This time they are asked simply to fry an egg (no fire). The
<BR>engineer just does it, kludging along; the physicist calculates
<BR>carefully and produces a carefully cooked egg; and the mathematician
<BR>lights a fire in the corner, and says \"I have reduced it to the
<BR>previous problem.\"
<BR>
<BR>-------------------------------------------------------------------------------
<BR>A physicist and a mathematician setting in a faculty lounge.
<BR>Suddenly, the coffee machine catches on fire. The physicist grabs a
<BR>bucket and leaps towards the sink, fills the bucket with water and
<BR>puts out the fire. The second day, the same two sit in the same
<BR>lounge. Again, the coffee machine catches on fire. This time, the
<BR>mathematician stands up, gets a bucket, hands the bucket to the
<BR>physicist, thus reducing the problem to a previously solved one.
<BR>
<BR>-------------------------------------------------------------------------------
<BR>An engineer, a mathematician, and a physicist are staying in three
<BR>adjoining cabins at a decrepit old motel.
<BR>
<BR>First the engineer\'s coffee maker catches fire on the bathroom vanity.
<BR>He smells the smoke, wakes up, unplugs it, throws it out the window,
<BR>and goes back to sleep.
<BR>
<BR>Later that night the physicist smells smoke too. He wakes up and sees
<BR>that a cigarette butt has set the trash can on fire. He says to
<BR>himself, \"Hmm. How does one put out a fire? One can reduce the
<BR>temperature of the fuel below the flash point, isolate the burning
<BR>material from oxygen, or both. This could be accomplished by applying
<BR>water.\" So he picks up the trash can, puts it in the shower stall,
<BR>turns on the water, and, when the fire is out, goes back to sleep.
<BR>
<BR>The mathematician, of course, has been watching all this out the
<BR>window. So later, when he finds that his pipe ashes have set the
<BR>bedsheet on fire, he is not in the least taken aback. He immediately
<BR>sees that the problem reduces to one that has already been solved and
<BR>goes back to sleep.
<BR>
<BR>-------------------------------------------------------------------------------
<BR>A mathematician and a physicist were asked the following question:
<BR>
<BR>Suppose you walked by a burning house and saw a hydrant and
<BR>a hose not connected to the hydrant. What would you do?
<BR>
<BR>P: I would attach the hose to the hydrant, turn on the water, and put out
<BR>the fire.
<BR>
<BR>M: I would attach the hose to the hydrant, turn on the water, and put out
<BR>the fire.
<BR>
<BR>Then they were asked this question:
<BR>
<BR>Suppose you walked by a house and saw a hose connected to
<BR>a hydrant. What would you do?
<BR>
<BR>P: I would keep walking, as there is no problem to solve.
<BR>
<BR>M: I would disconnect the hose from the hydrant and set the house on fire,
<BR>reducing the problem to a previously solved form.
<BR>
<BR>-------------------------------------------------------------------------------
<BR>There were two men trying to decide what to do for a living. They
<BR>went to see a counselor, and he decided that they had good problem
<BR>solving skills.
<BR>
<BR>He tried a test to narrow the area of specialty. He put each man in a
<BR>room with a stove, a table, and a pot of water on the table. He said
<BR>\"Boil the water\". Both men moved the pot from the table to the stove
<BR>and turned on the burner to boil the water. Next, he put them into a
<BR>room with a stove, a table, and a pot of water on the floor. Again,
<BR>he said \"Boil the water\". The first man put the pot on the stove and
<BR>turned on the burner. The counselor told him to be an Engineer,
<BR>because he could solve each problem individually. The second man
<BR>moved the pot from the floor to the table, and then moved the pot from
<BR>the table to the stove and turned on the burner. The counselor told
<BR>him to be a mathematician because he reduced the problem to a
<BR>previously solved problem.
<BR>
<BR>-------------------------------------------------------------------------------
<BR>So a mathematician, an engineer, and a physicist are out hunting
<BR>together. They spy a deer(*) in the woods.
<BR>
<BR>The physicist calculates the velocity of the deer and the effect of
<BR>gravity on the bullet, aims his rifle and fires. Alas, he misses; the
<BR>bullet passes three feet behind the deer. The deer bolts some yards,
<BR>but comes to a halt, still within sight of the trio.
<BR>
<BR>\"Shame you missed,\" comments the engineer, \"but of course with an
<BR>ordinary gun, one would expect that.\" He then levels his special
<BR>deer-hunting gun, which he rigged together from an ordinary rifle, a
<BR>sextant, a compass, a barometer, and a bunch of flashing lights which
<BR>don\'t do anything but impress onlookers, and fires. Alas, his bullet
<BR>passes three feet in front of the deer, who by this time wises up and
<BR>vanishes for good.
<BR>
<BR>\"Well,\" says the physicist, \"your contraption didn\'t get it either.\"
<BR>
<BR>\"What do you mean?\" pipes up the mathematician. \"Between the two of
<BR>you, that was a perfect shot!\"
<BR>
<BR>----------
<BR>
<BR>(*) How they knew it was a deer:
<BR>
<BR>The physicist observed that it behaved in a deer-like manner, so it
<BR>must be a deer.
<BR>
<BR>The mathematician asked the physicist what it was, thereby reducing it
<BR>to a previously solved problem.
<BR>
<BR>The engineer was in the woods to hunt deer, therefore it was a deer.
<BR>
<BR>-------------------------------------------------------------------------------
<BR>A computer scientist, mathematician, a physicist, and an engineer were
<BR>travelling through Scotland when they saw a black sheep through the
<BR>window of the train.
<BR>
<BR>\"Aha,\" says the engineer, \"I see that Scottish sheep are black.\"
<BR>
<BR>\"Hmm,\" says the physicist, \"You mean that some Scottish sheep are
<BR>black.\"
<BR>
<BR>\"No,\" says the mathematician, \"All we know is that there is at least
<BR>one sheep in Scotland, and that at least one side of that one sheep is
<BR>black!\"
<BR>
<BR>\"Oh, no!\" shouts the computer scientist, \"A special case!\"
<BR>
<BR>-------------------------------------------------------------------------------
<BR>A Mathematician (M) and an Engineer (E) attend a lecture by a
<BR>Physicist. The topic concerns Kulza-Klein theories involving physical
<BR>processes that occur in spaces with dimensions of 11, 12 and even
<BR>higher. The M is sitting, clearly enjoying the lecture, while the E
<BR>is frowning and looking generally confused and puzzled. By the end
<BR>the E has a terrible headache. At the end, the M comments about the
<BR>wonderful lecture. The E says \"How do you understand this stuff?\"
<BR>M: \"I just visualize the process.\"
<BR>E: \"How can you POSSIBLY visualize something that occurs in
<BR>11-dimensional space?\"
<BR>M: \"Easy, first visualize it in N-dimensional space, then let N go to 11.\"
<BR>
<BR>-------------------------------------------------------------------------------
<BR>What is \"pi\"?
<BR>
<BR>Mathematician: Pi is the number expressing the relationship between the
<BR>circumference of a circle and its diameter.
<BR>
<BR>Physicist: Pi is 3.1415927 plus or minus 0.00000005
<BR>
<BR>Engineer: Pi is about 3.
<BR>
<BR>-------------------------------------------------------------------------------
<BR>When considering the behaviour of a howitzer:
<BR>
<BR>A mathematician will be able to calculate where the shell will land.
<BR>
<BR>A physicist will be able to explain how the shell gets there.
<BR>
<BR>An engineer will stand there and try to catch it.
<BR>
<BR>-------------------------------------------------------------------------------
<BR>An engineer, a physicist and a mathematician find themselves in an
<BR>anecdote, indeed an anecdote quite similar to many that you have no
<BR>doubt already heard. After some observations and rough calculations
<BR>the engineer realizes the situation and starts laughing. A few
<BR>minutes later the physicist understands too and chuckles to himself
<BR>happily as he now has enough experimental evidence to publish a paper.
<BR>
<BR>This leaves the mathematician somewhat perplexed, as he had observed
<BR>right away that he was the subject of an anecdote, and deduced quite
<BR>rapidly the presence of humour from similar anecdotes, but considers
<BR>this anecdote to be too trivial a corollary to be significant, let
<BR>alone funny.
<BR>
<BR>-------------------------------------------------------------------------------
<BR>Q: What\'s purple and commutes?
<BR>A: An abelian grape.
<BR>
<BR>Q: Why did the mathematician name his dog \"Cauchy\"?
<BR>A: Because he left a residue at every pole.
<BR>
<BR>Q: Why is it that the more accuracy you demand from an interpolation
<BR>function, the more expensive it becomes to compute?
<BR>A: That\'s the Law of Spline Demand.
<BR>
<BR>Q: How many mathematicians does it take to screw in a lightbulb?
<BR>A: One, who gives it to six Californians, thereby reducing it to an
<BR>earlier riddle.
<BR>-- from a button I bought at Nancy Lebowitz\'s table at Boskone
<BR>
<BR>Q: What do a mathematician and a physicist [or engineer, or musician,
<BR>or whatever the profession of the person addressed] have in common?
<BR>A: They are both stupid, with the exception of the mathematician.
<BR>
<BR>Q: What do you call a teapot of boiling water on top of mount everest?
<BR>A: A high-pot-in-use
<BR>
<BR>Q: What do you call a broken record?
<BR>A: A Decca-gone
<BR>
<BR>Q: What do you get when you cross 50 female pigs and 50 male deer?
<BR>A: One hundred sows-and-bucks
<BR>
<BR>Q: Why did the chicken cross the Moebius strip?
<BR>A: To get to the other ... er, um ...
<BR>
<BR>Q: What is the world\'s longest song?
<BR>A: \"Aleph-nought Bottles of Beer on the Wall.\"
<BR>
<BR>Q: What does a mathematician do when he\'s constipated?
<BR>A: He works it out with a pencil.
<BR>
<BR>Q: What\'s yellow and equivalent to the Axiom of Choice.
<BR>A: Zorn\'s Lemon.
<BR>
<BR>Q: What do you get if you cross an elephant with a zebra.
<BR>A: Elephant zebra sin theta.
<BR>
<BR>Q: What do you get if you cross an elephant with a mountain climber.
<BR>A: You can\'t do that. A mountain climber is a scalar.
<BR>
<BR>Q: What do you get when you cross an elephant with a banana?
<BR>A: Elephant banana sine theta in a direction mutually perpendicular to
<BR>the two as determined by the right hand rule.
<BR>
<BR>Q: To what question is the answer \"9W.\"
<BR>A: \"Dr. Wiener, do you spell your name with a V?\"
<BR></DIV>
<BR>viplasent?
<BR>